Electron. J. Diff. Equ., Vol. 2016 (2016), No. 167, pp. 1-11.

Existence of infinitely many solutions for semilinear elliptic equations

Hui-Lan Pan, Chun-Lei Tang

Abstract:
In this article, we study the existence and infinitely many solutions for the elliptic boundary-value problem
$$\displaylines{ -\Delta u+a(x)u=f(x,u) \quad\text{in }\Omega, \cr u=0 \quad\text{on }\partial\Omega. }$$
Our main tools are the local linking and symmetric mountain pass theorem in critical point theory.

Submitted April 7, 2016. Published June 29, 2016.
Math Subject Classifications: 35J61, 35D30, 35J20.
Key Words: Super-quadratic condition; variational method; Cerami condition; critical point theory.

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Hui-Lan Pan
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: panhuilanswedu@163.com
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: tangcl@swu.edu.cn

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