An Improved Fountain Theorem and Its Application

Abstract

The main aim of the paper is to prove a fountain theorem without assuming the τ-upper semi-continuity condition on the variational functional. Using this improved fountain theorem, we may deal with more general strongly indefinite elliptic problems with various sign-changing nonlinear terms. As an application, we obtain infinitely many solutions for a semilinear Schrödinger equation with strongly indefinite structure and sign-changing nonlinearity.

Keywords

• fountain theorem
• strongly indefinite functional
• elliptic equation
• sign-changing potentials
• infinitely many solutions
• 35j20
• 35j60
• 35q55
• 58e05