Electron. J. Diff. Equ., Vol. 2014 (2014), No. 140, pp. 1-13.

Multiplicity of solutions for elliptic boundary value problems

Yiwei Ye, Chun-Lei Tang

Abstract:
In this article, we study the existence of infinitely many solutions for the semilinear elliptic equation $-\Delta u+a(x)u=f(x,u)$ in a bounded domain of $\mathbb{R}^N$ $(N\geq 3)$ with the Dirichlet boundary conditions, where the primitive of the nonlinearity f is either superquadratic at infinity or subquadratic at zero.

Submitted September 1, 2013. Published June 16, 2014.
Math Subject Classifications: 34C25, 35B38, 47J30.
Key Words: Elliptic boundary value problems; critical points; Cerami sequence; fountain theorem; symmetric mountain pass lemma.

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  Yiwei Ye
School of Mathematics and Statistics, Southwest University
Chongqing 400715, China
email: yeyiwei2011@126.com
Chun-Lei Tang
School of Mathematics and Statistics, Southwest University
Chongqing 400715, China
Phone +86 23 68253135, fax +86 23 68253135
email: tangcl@swu.edu.cn

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