Infinitely many solutions for semilinear Δλ-Laplace equations with sign-changing potential and nonlinearity

Abstract

In this paper, we prove the existence of infinitely many solutions for the following class of boundary value elliptic problems where Ω is a bounded domain in RN (N ≥ 2), Δλ is a strongly degenerate elliptic operator, V (x) is allowing to be sign-changing and f is a function with a more general super-quadratic growth, which is weaker than the Ambrosetti-Rabinowitz type condition.