In this paper, we study the multiplicity of solutions for a class of noncooperative p-Laplacian operator elliptic system. Under suitable assumptions, we obtain a sequence of solutions by using the limit index theory.
Mots clés : p-laplacian operator, limit index, critical growth, concentration-compactness principle
@article{COCV_2012__18_4_930_0, author = {Liang, Sihua and Zhang, Jihui}, title = {Multiplicity of solutions for the noncooperative $p$-laplacian operator elliptic system with nonlinear boundary conditions}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {930--940}, publisher = {EDP-Sciences}, volume = {18}, number = {4}, year = {2012}, doi = {10.1051/cocv/2011189}, zbl = {1276.35091}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2011189/} }
TY - JOUR AU - Liang, Sihua AU - Zhang, Jihui TI - Multiplicity of solutions for the noncooperative $p$-laplacian operator elliptic system with nonlinear boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 930 EP - 940 VL - 18 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2011189/ DO - 10.1051/cocv/2011189 LA - en ID - COCV_2012__18_4_930_0 ER -
%0 Journal Article %A Liang, Sihua %A Zhang, Jihui %T Multiplicity of solutions for the noncooperative $p$-laplacian operator elliptic system with nonlinear boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 930-940 %V 18 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2011189/ %R 10.1051/cocv/2011189 %G en %F COCV_2012__18_4_930_0
Liang, Sihua; Zhang, Jihui. Multiplicity of solutions for the noncooperative $p$-laplacian operator elliptic system with nonlinear boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 930-940. doi : 10.1051/cocv/2011189. http://www.numdam.org/articles/10.1051/cocv/2011189/
[1] On critical point theory for indefinite functionals in presence of symmetries. Trans. Amer. Math. Soc. 274 (1982) 533-572. | MR | Zbl
,[2] Positive solutions of nonlinear elliptic equations involving critical exponents. Comm. Pure Appl. Math. 34 (1983) 437-477. | MR | Zbl
and ,[3] On the solutions to some elliptic equations with nonlinear boundary conditions. Advances Differential Equations 1 (1996) 91-110. | MR | Zbl
, and ,[4] Existence results for the p-Laplacian with nonlinear boundary conditions. J. Math. Anal. Appl. 263 (2001) 195-223. | MR | Zbl
and ,[5] Existence results for a Hamiltonian elliptic system with nonlinear boundary conditions. Electron. J. Differential Equations 1999 (1999) 1-15. | MR | Zbl
, and ,[6] Multiplicity of solutions for a noncooperative p-Laplacian elliptic system in RN. J. Differential Equations 215 (2005) 206-223. | MR | Zbl
and ,[7] Some remarks on the Lusternik-Schnirelman method for non-differentiable functionals invariant with respect to a finite group action. Rocky Mt. J. Math. 20 (1990) 1041-1049. | MR | Zbl
and ,[8] A limit index theory and its application. Nonlinear Anal. 25 (1995) 1371-1389. | MR | Zbl
,[9] Multiplicity of solutions for a noncooperative elliptic system with critical Sobolev exponent. Z. Angew. Math. Phys. 60 (2009) 402-415. | MR | Zbl
and ,[10] Classical Banach Spaces I. Springer, Berlin (1977). | MR | Zbl
and ,[11] The concentration-compactness principle in the caculus of variation : the limit case, I. Rev. Mat. Ibero. 1 (1985) 45-120. | Zbl
,[12] The concentration-compactness principle in the caculus of variation : the limit case, II. Rev. Mat. Ibero. 1 (1985) 145-201. | MR | Zbl
,[13] Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition, Electron. J. Differential Equations 10 (1998) 1-13. | MR | Zbl
,[14] Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions. Differential Integral Equations 8 (1995) 1911-1922. | MR | Zbl
,[15] Interpolation Theory, Function Spaces, Differential Operators. North- Holland, Amsterdam (1978). | MR | Zbl
,[16] Minimax Theorems. Birkhäuser, Boston (1996). | MR | Zbl
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