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Four positive solutions of a quasilinear elliptic equation in $ R^N$
1. | School of Mathematics and Statistics, Southwest University, Chongqing 400715, China |
References:
[1] |
S. Adachi and K. Tanaka, Four positive solutions for the semilinear elliptic equation: $-\Delta u+u=a(x)u^p+f(x)$ in $R^N$, Calc. Var. Partial Differential Equations, 11 (2000), 63-95.
doi: 10.1007/s005260050003. |
[2] |
A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122 (1994), 519-543.
doi: 10.1006/jfan.1994.1078. |
[3] |
M. Badiale and G. Citti, Concentration compactness principle and quasilinear elliptic equations in $R^n$, Comm. Partial Differential Equations, 16 (1991), 1795-1818.
doi: 10.1080/03605309108820823. |
[4] |
H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88 (1983), 486-490.
doi: 10.2307/2044999. |
[5] |
J. Chabrowski and J. M. Bezzera do Ó, On semilinear elliptic equations involving concave and convex nonlinearities, Math. Nachr., 233/234 (2002), 55-76.
doi: 10.1002/1522-2616(200201)233:1<55::AID-MANA55>3.3.CO;2-I. |
[6] |
K.-C. Chang, "Infinite-dimensional Morse Theory and Multiple Solution Problems,'' Progress in Nonlinear Differential Equations and their Applications, 6. Birkhäuser Boston Inc., Boston, MA, 1993. |
[7] |
L. Damascelli, F. Pacella and M. Ramaswamy, Symmetry of ground states of $p$-Laplace equations via the moving plane method, Arch. Ration. Mech. Anal., 148 (1999), 291-308.
doi: 10.1007/s002050050163. |
[8] |
D. G. De Figueiredo, J.-P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems, J. Funct. Anal., 199 (2003), 452-467.
doi: 10.1016/S0022-1236(02)00060-5. |
[9] |
I. Ekeland, On the variational principle, J. Math. Anal. Appl., 47 (1974), 324-353. |
[10] |
F. Gazzola, B. Peletier, P. Pucci and J. Serrin, Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters. {II}, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 947-974.
doi: 10.1016/S0294-1449(03)00013-1. |
[11] |
T.-S. Hsu and H.-L. Lin, Four positive solutions of semilinear elliptic equations involving concave and convex nonlinearities in $R^N$, J. Math. Anal. Appl., 365 (2010), 758-775.
doi: 10.1016/j.jmaa.2009.12.004. |
[12] |
Y. Li and C. Zhao, A note on exponential decay properties of ground states for quasilinear elliptic equations, Proc. Amer. Math. Soc., 133 (2005), 2005-2012 (electronic).
doi: 10.1090/S0002-9939-05-07870-6. |
[13] |
T.-F. Wu, On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function, J. Math. Anal. Appl., 318 (2006), 253-270.
doi: 10.1016/j.jmaa.2005.05.057. |
[14] |
T.-F. Wu, Multiplicity of positive solution of $p$-Laplacian problems with sign-changing weight functions, Int. J. Math. Anal. (Ruse), 1 (2007), 557-563. |
[15] |
T.-F. Wu, Multiple positive solutions for a class of concave-convex elliptic problems in $R^N$ involving sign-changing weight, J. Funct. Anal., 258 (2010), 99-131.
doi: 10.1016/j.jfa.2009.08.005. |
show all references
References:
[1] |
S. Adachi and K. Tanaka, Four positive solutions for the semilinear elliptic equation: $-\Delta u+u=a(x)u^p+f(x)$ in $R^N$, Calc. Var. Partial Differential Equations, 11 (2000), 63-95.
doi: 10.1007/s005260050003. |
[2] |
A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122 (1994), 519-543.
doi: 10.1006/jfan.1994.1078. |
[3] |
M. Badiale and G. Citti, Concentration compactness principle and quasilinear elliptic equations in $R^n$, Comm. Partial Differential Equations, 16 (1991), 1795-1818.
doi: 10.1080/03605309108820823. |
[4] |
H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88 (1983), 486-490.
doi: 10.2307/2044999. |
[5] |
J. Chabrowski and J. M. Bezzera do Ó, On semilinear elliptic equations involving concave and convex nonlinearities, Math. Nachr., 233/234 (2002), 55-76.
doi: 10.1002/1522-2616(200201)233:1<55::AID-MANA55>3.3.CO;2-I. |
[6] |
K.-C. Chang, "Infinite-dimensional Morse Theory and Multiple Solution Problems,'' Progress in Nonlinear Differential Equations and their Applications, 6. Birkhäuser Boston Inc., Boston, MA, 1993. |
[7] |
L. Damascelli, F. Pacella and M. Ramaswamy, Symmetry of ground states of $p$-Laplace equations via the moving plane method, Arch. Ration. Mech. Anal., 148 (1999), 291-308.
doi: 10.1007/s002050050163. |
[8] |
D. G. De Figueiredo, J.-P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems, J. Funct. Anal., 199 (2003), 452-467.
doi: 10.1016/S0022-1236(02)00060-5. |
[9] |
I. Ekeland, On the variational principle, J. Math. Anal. Appl., 47 (1974), 324-353. |
[10] |
F. Gazzola, B. Peletier, P. Pucci and J. Serrin, Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters. {II}, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 947-974.
doi: 10.1016/S0294-1449(03)00013-1. |
[11] |
T.-S. Hsu and H.-L. Lin, Four positive solutions of semilinear elliptic equations involving concave and convex nonlinearities in $R^N$, J. Math. Anal. Appl., 365 (2010), 758-775.
doi: 10.1016/j.jmaa.2009.12.004. |
[12] |
Y. Li and C. Zhao, A note on exponential decay properties of ground states for quasilinear elliptic equations, Proc. Amer. Math. Soc., 133 (2005), 2005-2012 (electronic).
doi: 10.1090/S0002-9939-05-07870-6. |
[13] |
T.-F. Wu, On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function, J. Math. Anal. Appl., 318 (2006), 253-270.
doi: 10.1016/j.jmaa.2005.05.057. |
[14] |
T.-F. Wu, Multiplicity of positive solution of $p$-Laplacian problems with sign-changing weight functions, Int. J. Math. Anal. (Ruse), 1 (2007), 557-563. |
[15] |
T.-F. Wu, Multiple positive solutions for a class of concave-convex elliptic problems in $R^N$ involving sign-changing weight, J. Funct. Anal., 258 (2010), 99-131.
doi: 10.1016/j.jfa.2009.08.005. |
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