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On symmetry results for elliptic equations with convex nonlinearities
1. | Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901 |
2. | Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, I-37134 Veron |
References:
[1] |
T. Bartsch and M. Degiovanni, Nodal solutions of nonlinear elliptic Dirichlet problems on radial domains, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 17 (2006), 69-85.
doi: 10.4171/RLM/454. |
[2] |
T. Bartsch, T. Weth and M. Willem, Partial symmetry of least energy nodal solutions to some variational problems, J. Anal. Math., 96 (2005), 1-18.
doi: 10.1007/BF02787822. |
[3] |
M. Colin, L. Jeanjean and M. Squassina, Stability and instability results for standing waves of quasi-linear Schrödinger equations, Nonlinearity, 23 (2010), 1353-1385.
doi: 10.1088/0951-7715/23/6/006. |
[4] |
M. Ghergu and V. Radulescu, "Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population Genetics," Springer Monographs in Mathematics, Springer Verlag, Heidelberg, xviii+392 pp., 2011. |
[5] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
doi: 10.1007/BF01221125. |
[6] |
F. Gladiali and M. Squassina, Uniqueness of ground states for a class of quasi-linear elliptic equations, Adv. Nonlinear Anal., 1 (2012), 159-179.
doi: 10.1515/ana-2011-0001. |
[7] |
F. Gladiali and M. Squassina, On explosive solutions for a class of quasi-linear elliptic equations,, Adv. Nonlinear Stud., ().
|
[8] |
F. Pacella, Symmetry results for solutions of semilinear elliptic equations with convex non-linearities, J. Funct. Anal., 192 (2002), 271-282.
doi: 10.1006/jfan.2001.3901. |
[9] |
F. Pacella and T. Weth, Symmetry of solutions to semilinear elliptic equations via Morse index, Proc. Amer. Math. Soc., 135 (2007), 1753-1762.
doi: 10.1090/S0002-9939-07-08652-2. |
[10] |
V. Radulescu, "Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods," Contemporary Mathematics and Its Applications, 6, Hindawi, 210 pp., 2008.
doi: 10.1155/9789774540394. |
[11] |
J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal., 43 (1971), 304-318.
doi: 10.1007/BF00250468. |
[12] |
D. Smets and M. Willem, Partial symmetry and asymptotic behaviour for some elliptic variational problems, Calc. Var. Partial Differential Equations, 18 (2003), 57-75.
doi: 10.1007/s00526-002-0180-y. |
[13] |
M. Squassina, Existence, multiplicity, perturbation, and concentration results for a class of quasi-linear elliptic problems, Electron. J. Differential Equations, Monograph 7, 2006, +213pp, Texas State University, USA. |
[14] |
M. Squassina, Symmetry in variational principles and applications, J. London Math. Soc., 85 (2012), 323-348.
doi: 10.1112/jlms/jdr046. |
show all references
References:
[1] |
T. Bartsch and M. Degiovanni, Nodal solutions of nonlinear elliptic Dirichlet problems on radial domains, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 17 (2006), 69-85.
doi: 10.4171/RLM/454. |
[2] |
T. Bartsch, T. Weth and M. Willem, Partial symmetry of least energy nodal solutions to some variational problems, J. Anal. Math., 96 (2005), 1-18.
doi: 10.1007/BF02787822. |
[3] |
M. Colin, L. Jeanjean and M. Squassina, Stability and instability results for standing waves of quasi-linear Schrödinger equations, Nonlinearity, 23 (2010), 1353-1385.
doi: 10.1088/0951-7715/23/6/006. |
[4] |
M. Ghergu and V. Radulescu, "Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population Genetics," Springer Monographs in Mathematics, Springer Verlag, Heidelberg, xviii+392 pp., 2011. |
[5] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
doi: 10.1007/BF01221125. |
[6] |
F. Gladiali and M. Squassina, Uniqueness of ground states for a class of quasi-linear elliptic equations, Adv. Nonlinear Anal., 1 (2012), 159-179.
doi: 10.1515/ana-2011-0001. |
[7] |
F. Gladiali and M. Squassina, On explosive solutions for a class of quasi-linear elliptic equations,, Adv. Nonlinear Stud., ().
|
[8] |
F. Pacella, Symmetry results for solutions of semilinear elliptic equations with convex non-linearities, J. Funct. Anal., 192 (2002), 271-282.
doi: 10.1006/jfan.2001.3901. |
[9] |
F. Pacella and T. Weth, Symmetry of solutions to semilinear elliptic equations via Morse index, Proc. Amer. Math. Soc., 135 (2007), 1753-1762.
doi: 10.1090/S0002-9939-07-08652-2. |
[10] |
V. Radulescu, "Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods," Contemporary Mathematics and Its Applications, 6, Hindawi, 210 pp., 2008.
doi: 10.1155/9789774540394. |
[11] |
J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal., 43 (1971), 304-318.
doi: 10.1007/BF00250468. |
[12] |
D. Smets and M. Willem, Partial symmetry and asymptotic behaviour for some elliptic variational problems, Calc. Var. Partial Differential Equations, 18 (2003), 57-75.
doi: 10.1007/s00526-002-0180-y. |
[13] |
M. Squassina, Existence, multiplicity, perturbation, and concentration results for a class of quasi-linear elliptic problems, Electron. J. Differential Equations, Monograph 7, 2006, +213pp, Texas State University, USA. |
[14] |
M. Squassina, Symmetry in variational principles and applications, J. London Math. Soc., 85 (2012), 323-348.
doi: 10.1112/jlms/jdr046. |
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