Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T03:50:22.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiplicity of solutions for the noncooperativep-Laplacian operator elliptic system with nonlinear boundaryconditions

Published online by Cambridge University Press:  16 January 2012

Sihua Liang  and
Jihui Zhang
Sihua Liang
Affiliation:
College of Mathematics, Changchun Normal University, Changchun 130032, Jilin, P.R. China. [email protected]
Jihui Zhang
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210046, P.R. China; [email protected]
Get access

Abstract

In this paper, we study the multiplicity of solutions for a class of noncooperativep-Laplacian operator elliptic system. Under suitable assumptions, weobtain a sequence of solutions by using the limit index theory.

Keywords

p-Laplacian operatorlimit indexcritical growthconcentration-compactness principle
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 930 - 940
Copyright
© EDP Sciences, SMAI, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benci, V., On critical point theory for indefinite functionals in presence of symmetries. Trans. Amer. Math. Soc. 274 (1982) 533–572. Google Scholar
Brézis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical exponents. Comm. Pure Appl. Math. 34 (1983) 437–477. Google Scholar
Chipot, M., Shafrir, I. and Fila, M., On the solutions to some elliptic equations with nonlinear boundary conditions. Advances Differential Equations 1 (1996) 91–110. Google Scholar
Fernández Bonder, J. and Rossi, J.D., Existence results for the p-Laplacian with nonlinear boundary conditions. J. Math. Anal. Appl. 263 (2001) 195–223. Google Scholar
Fernández Bonder, J., Pinasco, J.P. and Rossi, J.D., Existence results for a Hamiltonian elliptic system with nonlinear boundary conditions. Electron. J. Differential Equations 1999 (1999) 1–15. Google Scholar
Huang, D.W. and Li, Y.Q., Multiplicity of solutions for a noncooperative p-Laplacian elliptic system in RN. J. Differential Equations 215 (2005) 206–223. Google Scholar
Krawcewicz, W. and Marzantowicz, W., 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. Google Scholar
Li, Y.Q., A limit index theory and its application. Nonlinear Anal. 25 (1995) 1371–1389. Google Scholar
Lin, F. and Li, Y.Q., Multiplicity of solutions for a noncooperative elliptic system with critical Sobolev exponent. Z. Angew. Math. Phys. 60 (2009) 402–415. Google Scholar
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Springer, Berlin (1977).
Lions, P.L., The concentration-compactness principle in the caculus of variation : the limit case, I. Rev. Mat. Ibero. 1 (1985) 45–120. Google Scholar
Lions, P.L., The concentration-compactness principle in the caculus of variation : the limit case, II. Rev. Mat. Ibero. 1 (1985) 145–201. Google Scholar
Pflüger, K., Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition, Electron. J. Differential Equations 10 (1998) 1–13. Google Scholar
Terraccini, S., Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions. Differential Integral Equations 8 (1995) 1911–1922. Google Scholar
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North- Holland, Amsterdam (1978).
M. Willem, Minimax Theorems. Birkhäuser, Boston (1996).