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Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems
1. | American Institute of Mathematical Sciences, P.O. Box 2604, Springfield, MO 65801 |
2. | Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780 |
References:
[1] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, The spectrum and an index formula for the Neumann $p$-Laplacian and multiple solutions for problems with a crossing nonlinearity,, Discrete Cont Dyn Systems, 25 (2009), 431.
|
[2] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, On a $p$-superlinear Neumann $p$-Laplacian equation, Topol., Methods Nonlin. Anal., 34 (2009), 111.
|
[3] |
A. Allendes and A. Quaas, Multiplicity results for extremal operators through bifurcation,, Discrete Cont Dyn Systems, 29 (2011), 51.
|
[4] |
D. Arcoya and D. Ruiz, The Ambrosetti-Prodi problem for the $p$-Laplace operator,, Comm. Part. Diff. Equs., 31 (2006), 849.
doi: 10.1080/03605300500394447. |
[5] |
V. Benci, P. D'Avenia, D. Fortunato and L. Pisani, Solitons in several space dimensions: Derrick's problem and infinitely many solutions,, Arch. Rational Mech. Anal., 154 (2000), 297.
doi: 10.1007/s002050000101. |
[6] |
R. Benguria, H. Brezis and E. H. Lieb, The Thomas-Fermi-von Weizsäcker theory of atoms and molecules,, Comm. Math. Physics, 79 (1981), 167.
doi: 10.1007/BF01942059. |
[7] |
H. Brezis and L. Nirenberg, $H^1$ versus $C^1$ local minimizers,, CRAS Paris t., 317 (1993), 465.
|
[8] |
S. Cano-Casanova, Coercivity of elliptic mixed boundary value problems in annulus of $\mathbbR^N$,, Discrete and Continuous Dynamical Systems, 32 (2012), 3819.
doi: 10.3934/dcds.2012.32.3819. |
[9] |
K. C. Chang, "Methods of Nonilnear Analysis,", Springer, (2005).
|
[10] |
S. Cingolani and M. Degiovanni, Nontrivial solutions for $p$-Laplacian equations with right hand side having $p$-linear growth,, Comm. Part. Diff. Equas., 30 (2005), 1191.
doi: 10.1080/03605300500257594. |
[11] |
S. Cingolani and G. Vannella, Critical groups computations on a class of Sobolev Banach spaces via Morse index,, ann. Inst. H. Poincare-AN, 20 (2003), 271.
|
[12] |
S. Cingolani and G. Vannella, Marino-Prodi perturbation type results and Morse indices of minimaz critical points for a class of functionals in Banach spaces,, Annali di Mat. Pura Appl., 186 (2007), 155.
doi: 10.1007/s10231-005-0176-2. |
[13] |
P. Clement, M.Garcia Huidobro, R. Manasevich and K. Schmitt, Mountain pass solutions for quasilinear elliptic equations,, Calc. Var., 11 (2000), 33.
doi: 10.1007/s005260050002. |
[14] |
D. Costa and C. Magalhaes, Existence results for perturbations of the $p$-Laplacian,, Nonlinear Anal., 24 (1995), 409.
doi: 10.1016/0362-546X(94)E0046-J. |
[15] |
M. Cuesta, D. deFigueiredo and J. P. Gossez, The beginning of the Fu$\brevec$ik spectrum for the $p$-Laplacian,, J. Diff. Equas., 159 (1999), 212.
doi: 10.1006/jdeq.1999.3645. |
[16] |
M. Cuesta and P. Takac, A strong comparison principle for positive solutions of degenerate elliptic equations,, Diff. Integ. Equas., 13 (2000), 721.
|
[17] |
N. Dancer, On domain perturbation for super-linear Neumann problems and a question of Y. Lou, W-M Ni and L. Su,, Discrete Cont Dyn Systems, 32 (2012), 3861.
|
[18] |
P. De Napoli and M. C. Mariani, Mountain pass solutions to equations of $p$-Laplacian type,, Nonlinear Anal., (2003), 1205.
doi: 10.1016/S0362-546X(03)00105-6. |
[19] |
M. Degiovanni and M. Scaglia, A variational approach to semilinear elliptic equations with measure data,, Discrete and Continuous Dynamical Systems, 31 (2011), 1233.
doi: 10.3934/dcds.2011.31.1233. |
[20] |
Y. Deng, S. Peng and L. Wang, Existence of multiple solutions for a nonhomogeneous semilinear elliptic equatio involving critical exponent,, Discrete Contin. Dynam. Systems, 32 (2012), 795.
|
[21] |
C. H. Derrick, Comments on nonlinear wave equations as model elementary particles,, J. Math. Phys., 5 (1964), 1252.
doi: 10.1063/1.1704233. |
[22] |
J. I. Diaz and J. E. Saa, Existence et unicité de solutions positives pour certaines equations elliptiques quasilineaires,, CRAS, 305 (1987), 521.
|
[23] |
N. Dunford and J.Schwartz, "Linear Operators I,", Wiley-Interscience, (). Google Scholar |
[24] |
G. Fei, On periodic solutions of superquadratic Hamiltonian systems,, Elec. J. Diff. Equas., 8 (2002), 1.
|
[25] |
D. deFigueiredo, Positive solutions of semilinear elliptic problems,, in, (1982), 34.
|
[26] |
M. Filippakis, A. Kristaly and N. S. Papageorgiou, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation,, Discrete Cont Dyn Systems, 24 (2009), 405.
doi: 10.3934/dcds.2009.24.405. |
[27] |
J. Garcia Azorero, J. Manfredi and I. Peral Alonso, Sobolev versus Hölder local minimizers and globla multiplicity for some quasilinear elliptic equations,, Comm. Contemp. Math., 2 (2000), 385.
doi: 10.1142/S0219199700000190. |
[28] |
L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis,", Chapman & Hall/CRC, (2006).
|
[29] |
L. Gasinski and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann $p$-Laplacian type equations,, Adv. Nonlin. Studies, 8 (2008), 843.
|
[30] |
L. Gasinski and N. S. Papageorgiou, Multiple solutions for nonlinear coersive problems with a nonhomogeneous differential operator and a nonsmooth potential,, Set Valued Var. Anal., 20 (2012), 417.
doi: 10.1007/s11228-011-0198-4. |
[31] |
D. Gilberg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order,", Springer, (1983).
doi: 10.1007/978-3-642-61798-0. |
[32] |
M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponents,, Nonlin. Anal., 13 (1989), 879.
doi: 10.1016/0362-546X(89)90020-5. |
[33] |
Z. Guo and Z. Liu, Perturbed elliptic equations with oscillatory nonlinearities,, Discrete Cont Dyn Systems, 32 (2012), 3567.
doi: 10.3934/dcds.2012.32.3567. |
[34] |
Z. Guo, Z. Liu, J. Wei and F. Zhou, Bifurcations of some elliptic problems with a singular nonlinearity via Morse index,, Comm. Pure. Appl. Anal., 10 (2011), 507.
doi: 10.3934/cpaa.2011.10.507. |
[35] |
Shouchuan Hu and N. S. Papageorgiou, Positive solutions for nonlinear hemivariational inequalities,, J. Math. Anal. Appl., 310 (2005), 161.
doi: 10.1016/j.jmaa.2005.01.051. |
[36] |
Shouchuan Hu and N. S. Papageorgiou, Nonlinear Neumann equations driven by a nonhomogeneous differential operator,, Comm. Pure Appl. Anal., 9 (2010), 1801.
|
[37] |
Shouchuan Hu and N. S. Papageorgiou, Double resonance for Dirichlet problems with unbounded indefinite potential and combined nonlinearities,, Comm. Pure Applied Anal., 11 (2012), 2005.
doi: 10.3934/cpaa.2012.11.2005. |
[38] |
J. Garcia Melian, J. Rossi and J. Sabina de Lis, A convex-concave problem with a parameter on the boundary condition,, Discrete Contin. Dynam. Systems, 32 (2012), 1095.
|
[39] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and applications to Landesmann-Lazer type problems in $\rn$,, Proc. Royal Soc. Edinburgh, 129A (1999), 767. Google Scholar |
[40] |
A. Kristaly, M. Mihaileseu and V. Radulescu, Two nontrivial solutions for a nonhomogeneous Neumann problem: an Orlicz-Sobolev space setting,, Proc. Royal. Soc. Edinburgh, 139A (2009), 367.
doi: 10.1017/S030821050700025X. |
[41] |
S. Kyritsi, D. O'Regan and N. S. Papageorgiou, Multiple solutions for resonant hemivariational inequalities via minimax methods,, Adv. Nonlin. Studies, 9 (2009), 453.
|
[42] |
S. Kyritsi and N. S. Papageorgiou, Multiple solutions for nonlinear elliptic equations with asymmetric reaction term,, Discrete Cont Dyn Systems, 33 (2013), 2469. Google Scholar |
[43] |
O. A. Ladyzhenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations,", Academic Press, (1968).
|
[44] |
G. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Uraltseva for elliptic equations,, Comm. Part. Diff. Equas., 16 (1991), 311.
doi: 10.1080/03605309108820761. |
[45] |
S. Li, S. Wu and H. Zhou, Solutions to semilinear elliptic problems with combined nonlinearities,, J. Diff. Equas., 185 (2002), 200.
doi: 10.1006/jdeq.2001.4167. |
[46] |
M. Mihailescu, Existence and multiplicity of weak solutions for a class of degenerate nonlinear ellipitc equations,, Boundary Value Problems, (2006), 1.
|
[47] |
M. Mihailescu and V. Radulescu, Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting,, J. Math. Anal. Appl., 330 (2007), 416.
doi: 10.1016/j.jmaa.2006.07.082. |
[48] |
M. L. Miotto, Multiple solutions for elliptic problems in $R^N$ with critical Spbolev exponent and weight function,, Comm. Pure Appl. Anal., 9 (2010), 233.
doi: 10.3934/cpaa.2010.9.233. |
[49] |
S. Miyajima, D. Motreanu and M. Tanaka, Multiple existence results of solutions for Neumann problems via super- and sub-solutions,, J. Functional Anal., 262 (2012), 1921.
doi: 10.1016/j.jfa.2011.11.028. |
[50] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, On $p$-Laplace equations with concave terms and asymmetric nonlinearities,, Proc. Royal Soc. Edinburgh, 141A (2011), 171.
doi: 10.1017/S0308210509001656. |
[51] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Multiple constant sign and nodal solutions for nonlinear Neumann eigenvalue problems,, Annali Scuola Normale Sup. Pisa, (2011), 729.
|
[52] |
D. Motreanu, D. O'Regan and N. S. Papageorgiou, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems,, Comm. Pure Appl. Anal., 10 (2011), 1791.
doi: 10.3934/cpaa.2011.10.1791. |
[53] |
D. Motreanu and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann problems,, J. Diff. Equas., 232 (2007), 1.
doi: 10.1016/j.jde.2006.09.008. |
[54] |
D. Motreanu and N. S. Papageorgiou, Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator,, Proc. Amer. Math. Soc., 139 (2011), 3527.
doi: 10.1090/S0002-9939-2011-10884-0. |
[55] |
N. S. Papageorgiou and S. Th. Kyritsi, "Handbook of Applied Analysis,", Springer, (2009).
|
[56] |
N. S. Papageorgiou and E. M. Rocha, On nonlinear parametric problems for $p$-Laplacian like operators,, RACSAM, 103 (2009), 177.
doi: 10.1007/BF03191850. |
[57] |
N. S. Papageorgiou, E. M. Rocha and V. Staicu, A multiplicity theorem for hemivariational inequalities with a $p$-Laplacian like differential operator,, Nonlin. Anal., 69 (2008), 1150.
doi: 10.1016/j.na.2007.06.023. |
[58] |
P. Pucci and J. Serrin, The strong maximum principle revisited,, J. Diff. Equas., 196 (2004), 1.
|
[59] |
P. Pucci and J. Serrin, "The Maximum Principle,", Birkhauser, (2007).
doi: 10.1016/j.jde.2004.09.002. |
[60] |
J. M. Rakotoson, Generalized eigenvalue problem for totally discontinuous operator,, Discrete Contin. Dynam. Systems, 28 (2010), 343.
doi: 10.3934/dcds.2010.28.343. |
[61] |
P. Roselli and B. Sciunzi, A strong comparison principle for the $p$-Laplacian,, Proc. Amer. Math. Soc., 135 (2007), 3217.
doi: 10.1090/S0002-9939-07-08847-8. |
[62] |
M. Sun, Multiplicity of solutions for a class of quasilinear elliptic equation at resonance,, J. Math. Anal. Appl., 386 (2012), 661.
doi: 10.1016/j.jmaa.2011.08.030. |
[63] |
J. Vazquez, A strong maximum principle for some quailinear elliptic equations,, Appl. Math. Optim., 12 (1984), 191.
doi: 10.1007/BF01449041. |
[64] |
R. Zhang, J. Chen and F. Zhan, Multiple solutions for superlinear elliptic systems of Hamiltonian type,, Discrete Cont Dyn Systems, 30 (2011), 1249.
doi: 10.3934/dcds.2011.30.1249. |
show all references
References:
[1] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, The spectrum and an index formula for the Neumann $p$-Laplacian and multiple solutions for problems with a crossing nonlinearity,, Discrete Cont Dyn Systems, 25 (2009), 431.
|
[2] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, On a $p$-superlinear Neumann $p$-Laplacian equation, Topol., Methods Nonlin. Anal., 34 (2009), 111.
|
[3] |
A. Allendes and A. Quaas, Multiplicity results for extremal operators through bifurcation,, Discrete Cont Dyn Systems, 29 (2011), 51.
|
[4] |
D. Arcoya and D. Ruiz, The Ambrosetti-Prodi problem for the $p$-Laplace operator,, Comm. Part. Diff. Equs., 31 (2006), 849.
doi: 10.1080/03605300500394447. |
[5] |
V. Benci, P. D'Avenia, D. Fortunato and L. Pisani, Solitons in several space dimensions: Derrick's problem and infinitely many solutions,, Arch. Rational Mech. Anal., 154 (2000), 297.
doi: 10.1007/s002050000101. |
[6] |
R. Benguria, H. Brezis and E. H. Lieb, The Thomas-Fermi-von Weizsäcker theory of atoms and molecules,, Comm. Math. Physics, 79 (1981), 167.
doi: 10.1007/BF01942059. |
[7] |
H. Brezis and L. Nirenberg, $H^1$ versus $C^1$ local minimizers,, CRAS Paris t., 317 (1993), 465.
|
[8] |
S. Cano-Casanova, Coercivity of elliptic mixed boundary value problems in annulus of $\mathbbR^N$,, Discrete and Continuous Dynamical Systems, 32 (2012), 3819.
doi: 10.3934/dcds.2012.32.3819. |
[9] |
K. C. Chang, "Methods of Nonilnear Analysis,", Springer, (2005).
|
[10] |
S. Cingolani and M. Degiovanni, Nontrivial solutions for $p$-Laplacian equations with right hand side having $p$-linear growth,, Comm. Part. Diff. Equas., 30 (2005), 1191.
doi: 10.1080/03605300500257594. |
[11] |
S. Cingolani and G. Vannella, Critical groups computations on a class of Sobolev Banach spaces via Morse index,, ann. Inst. H. Poincare-AN, 20 (2003), 271.
|
[12] |
S. Cingolani and G. Vannella, Marino-Prodi perturbation type results and Morse indices of minimaz critical points for a class of functionals in Banach spaces,, Annali di Mat. Pura Appl., 186 (2007), 155.
doi: 10.1007/s10231-005-0176-2. |
[13] |
P. Clement, M.Garcia Huidobro, R. Manasevich and K. Schmitt, Mountain pass solutions for quasilinear elliptic equations,, Calc. Var., 11 (2000), 33.
doi: 10.1007/s005260050002. |
[14] |
D. Costa and C. Magalhaes, Existence results for perturbations of the $p$-Laplacian,, Nonlinear Anal., 24 (1995), 409.
doi: 10.1016/0362-546X(94)E0046-J. |
[15] |
M. Cuesta, D. deFigueiredo and J. P. Gossez, The beginning of the Fu$\brevec$ik spectrum for the $p$-Laplacian,, J. Diff. Equas., 159 (1999), 212.
doi: 10.1006/jdeq.1999.3645. |
[16] |
M. Cuesta and P. Takac, A strong comparison principle for positive solutions of degenerate elliptic equations,, Diff. Integ. Equas., 13 (2000), 721.
|
[17] |
N. Dancer, On domain perturbation for super-linear Neumann problems and a question of Y. Lou, W-M Ni and L. Su,, Discrete Cont Dyn Systems, 32 (2012), 3861.
|
[18] |
P. De Napoli and M. C. Mariani, Mountain pass solutions to equations of $p$-Laplacian type,, Nonlinear Anal., (2003), 1205.
doi: 10.1016/S0362-546X(03)00105-6. |
[19] |
M. Degiovanni and M. Scaglia, A variational approach to semilinear elliptic equations with measure data,, Discrete and Continuous Dynamical Systems, 31 (2011), 1233.
doi: 10.3934/dcds.2011.31.1233. |
[20] |
Y. Deng, S. Peng and L. Wang, Existence of multiple solutions for a nonhomogeneous semilinear elliptic equatio involving critical exponent,, Discrete Contin. Dynam. Systems, 32 (2012), 795.
|
[21] |
C. H. Derrick, Comments on nonlinear wave equations as model elementary particles,, J. Math. Phys., 5 (1964), 1252.
doi: 10.1063/1.1704233. |
[22] |
J. I. Diaz and J. E. Saa, Existence et unicité de solutions positives pour certaines equations elliptiques quasilineaires,, CRAS, 305 (1987), 521.
|
[23] |
N. Dunford and J.Schwartz, "Linear Operators I,", Wiley-Interscience, (). Google Scholar |
[24] |
G. Fei, On periodic solutions of superquadratic Hamiltonian systems,, Elec. J. Diff. Equas., 8 (2002), 1.
|
[25] |
D. deFigueiredo, Positive solutions of semilinear elliptic problems,, in, (1982), 34.
|
[26] |
M. Filippakis, A. Kristaly and N. S. Papageorgiou, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation,, Discrete Cont Dyn Systems, 24 (2009), 405.
doi: 10.3934/dcds.2009.24.405. |
[27] |
J. Garcia Azorero, J. Manfredi and I. Peral Alonso, Sobolev versus Hölder local minimizers and globla multiplicity for some quasilinear elliptic equations,, Comm. Contemp. Math., 2 (2000), 385.
doi: 10.1142/S0219199700000190. |
[28] |
L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis,", Chapman & Hall/CRC, (2006).
|
[29] |
L. Gasinski and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann $p$-Laplacian type equations,, Adv. Nonlin. Studies, 8 (2008), 843.
|
[30] |
L. Gasinski and N. S. Papageorgiou, Multiple solutions for nonlinear coersive problems with a nonhomogeneous differential operator and a nonsmooth potential,, Set Valued Var. Anal., 20 (2012), 417.
doi: 10.1007/s11228-011-0198-4. |
[31] |
D. Gilberg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order,", Springer, (1983).
doi: 10.1007/978-3-642-61798-0. |
[32] |
M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponents,, Nonlin. Anal., 13 (1989), 879.
doi: 10.1016/0362-546X(89)90020-5. |
[33] |
Z. Guo and Z. Liu, Perturbed elliptic equations with oscillatory nonlinearities,, Discrete Cont Dyn Systems, 32 (2012), 3567.
doi: 10.3934/dcds.2012.32.3567. |
[34] |
Z. Guo, Z. Liu, J. Wei and F. Zhou, Bifurcations of some elliptic problems with a singular nonlinearity via Morse index,, Comm. Pure. Appl. Anal., 10 (2011), 507.
doi: 10.3934/cpaa.2011.10.507. |
[35] |
Shouchuan Hu and N. S. Papageorgiou, Positive solutions for nonlinear hemivariational inequalities,, J. Math. Anal. Appl., 310 (2005), 161.
doi: 10.1016/j.jmaa.2005.01.051. |
[36] |
Shouchuan Hu and N. S. Papageorgiou, Nonlinear Neumann equations driven by a nonhomogeneous differential operator,, Comm. Pure Appl. Anal., 9 (2010), 1801.
|
[37] |
Shouchuan Hu and N. S. Papageorgiou, Double resonance for Dirichlet problems with unbounded indefinite potential and combined nonlinearities,, Comm. Pure Applied Anal., 11 (2012), 2005.
doi: 10.3934/cpaa.2012.11.2005. |
[38] |
J. Garcia Melian, J. Rossi and J. Sabina de Lis, A convex-concave problem with a parameter on the boundary condition,, Discrete Contin. Dynam. Systems, 32 (2012), 1095.
|
[39] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and applications to Landesmann-Lazer type problems in $\rn$,, Proc. Royal Soc. Edinburgh, 129A (1999), 767. Google Scholar |
[40] |
A. Kristaly, M. Mihaileseu and V. Radulescu, Two nontrivial solutions for a nonhomogeneous Neumann problem: an Orlicz-Sobolev space setting,, Proc. Royal. Soc. Edinburgh, 139A (2009), 367.
doi: 10.1017/S030821050700025X. |
[41] |
S. Kyritsi, D. O'Regan and N. S. Papageorgiou, Multiple solutions for resonant hemivariational inequalities via minimax methods,, Adv. Nonlin. Studies, 9 (2009), 453.
|
[42] |
S. Kyritsi and N. S. Papageorgiou, Multiple solutions for nonlinear elliptic equations with asymmetric reaction term,, Discrete Cont Dyn Systems, 33 (2013), 2469. Google Scholar |
[43] |
O. A. Ladyzhenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations,", Academic Press, (1968).
|
[44] |
G. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Uraltseva for elliptic equations,, Comm. Part. Diff. Equas., 16 (1991), 311.
doi: 10.1080/03605309108820761. |
[45] |
S. Li, S. Wu and H. Zhou, Solutions to semilinear elliptic problems with combined nonlinearities,, J. Diff. Equas., 185 (2002), 200.
doi: 10.1006/jdeq.2001.4167. |
[46] |
M. Mihailescu, Existence and multiplicity of weak solutions for a class of degenerate nonlinear ellipitc equations,, Boundary Value Problems, (2006), 1.
|
[47] |
M. Mihailescu and V. Radulescu, Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting,, J. Math. Anal. Appl., 330 (2007), 416.
doi: 10.1016/j.jmaa.2006.07.082. |
[48] |
M. L. Miotto, Multiple solutions for elliptic problems in $R^N$ with critical Spbolev exponent and weight function,, Comm. Pure Appl. Anal., 9 (2010), 233.
doi: 10.3934/cpaa.2010.9.233. |
[49] |
S. Miyajima, D. Motreanu and M. Tanaka, Multiple existence results of solutions for Neumann problems via super- and sub-solutions,, J. Functional Anal., 262 (2012), 1921.
doi: 10.1016/j.jfa.2011.11.028. |
[50] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, On $p$-Laplace equations with concave terms and asymmetric nonlinearities,, Proc. Royal Soc. Edinburgh, 141A (2011), 171.
doi: 10.1017/S0308210509001656. |
[51] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Multiple constant sign and nodal solutions for nonlinear Neumann eigenvalue problems,, Annali Scuola Normale Sup. Pisa, (2011), 729.
|
[52] |
D. Motreanu, D. O'Regan and N. S. Papageorgiou, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems,, Comm. Pure Appl. Anal., 10 (2011), 1791.
doi: 10.3934/cpaa.2011.10.1791. |
[53] |
D. Motreanu and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann problems,, J. Diff. Equas., 232 (2007), 1.
doi: 10.1016/j.jde.2006.09.008. |
[54] |
D. Motreanu and N. S. Papageorgiou, Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator,, Proc. Amer. Math. Soc., 139 (2011), 3527.
doi: 10.1090/S0002-9939-2011-10884-0. |
[55] |
N. S. Papageorgiou and S. Th. Kyritsi, "Handbook of Applied Analysis,", Springer, (2009).
|
[56] |
N. S. Papageorgiou and E. M. Rocha, On nonlinear parametric problems for $p$-Laplacian like operators,, RACSAM, 103 (2009), 177.
doi: 10.1007/BF03191850. |
[57] |
N. S. Papageorgiou, E. M. Rocha and V. Staicu, A multiplicity theorem for hemivariational inequalities with a $p$-Laplacian like differential operator,, Nonlin. Anal., 69 (2008), 1150.
doi: 10.1016/j.na.2007.06.023. |
[58] |
P. Pucci and J. Serrin, The strong maximum principle revisited,, J. Diff. Equas., 196 (2004), 1.
|
[59] |
P. Pucci and J. Serrin, "The Maximum Principle,", Birkhauser, (2007).
doi: 10.1016/j.jde.2004.09.002. |
[60] |
J. M. Rakotoson, Generalized eigenvalue problem for totally discontinuous operator,, Discrete Contin. Dynam. Systems, 28 (2010), 343.
doi: 10.3934/dcds.2010.28.343. |
[61] |
P. Roselli and B. Sciunzi, A strong comparison principle for the $p$-Laplacian,, Proc. Amer. Math. Soc., 135 (2007), 3217.
doi: 10.1090/S0002-9939-07-08847-8. |
[62] |
M. Sun, Multiplicity of solutions for a class of quasilinear elliptic equation at resonance,, J. Math. Anal. Appl., 386 (2012), 661.
doi: 10.1016/j.jmaa.2011.08.030. |
[63] |
J. Vazquez, A strong maximum principle for some quailinear elliptic equations,, Appl. Math. Optim., 12 (1984), 191.
doi: 10.1007/BF01449041. |
[64] |
R. Zhang, J. Chen and F. Zhan, Multiple solutions for superlinear elliptic systems of Hamiltonian type,, Discrete Cont Dyn Systems, 30 (2011), 1249.
doi: 10.3934/dcds.2011.30.1249. |
[1] |
Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 |
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Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 |
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Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 |
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Giovanni Cimatti. Forced periodic solutions for piezoelectric crystals. Communications on Pure & Applied Analysis, 2005, 4 (2) : 475-485. doi: 10.3934/cpaa.2005.4.475 |
[5] |
Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810 |
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Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 |
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Ian Schindler, Kyril Tintarev. Mountain pass solutions to semilinear problems with critical nonlinearity. Conference Publications, 2007, 2007 (Special) : 912-919. doi: 10.3934/proc.2007.2007.912 |
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Shu-Yu Hsu. Existence and properties of ancient solutions of the Yamabe flow. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 91-129. doi: 10.3934/dcds.2018005 |
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Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817 |
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Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 |
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Palash Sarkar, Subhadip Singha. Verifying solutions to LWE with implications for concrete security. Advances in Mathematics of Communications, 2021, 15 (2) : 257-266. doi: 10.3934/amc.2020057 |
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Haibo Cui, Haiyan Yin. Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020210 |
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Yanqin Fang, Jihui Zhang. Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1267-1279. doi: 10.3934/cpaa.2011.10.1267 |
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Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309 |
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Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037 |
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Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
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Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
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Arseny Egorov. Morse coding for a Fuchsian group of finite covolume. Journal of Modern Dynamics, 2009, 3 (4) : 637-646. doi: 10.3934/jmd.2009.3.637 |
[19] |
Valeria Chiado Piat, Sergey S. Nazarov, Andrey Piatnitski. Steklov problems in perforated domains with a coefficient of indefinite sign. Networks & Heterogeneous Media, 2012, 7 (1) : 151-178. doi: 10.3934/nhm.2012.7.151 |
[20] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
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