Existence of infinitely many solutions for semilinear elliptic equations

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.

Keywords

• Super-quadratic condition
• variational method
• Cerami condition
• critical point theory