Multiple solutions for quasilinear elliptic equations with sign-changing potential

Abstract

In this article, we study the quasilinear elliptic equation $$ -\Delta_{p} u-(\Delta_{p}u^{2})u+ V (x)|u|^{p-2}u=g(x,u), \quad x\in \mathbb{R}^N, $$ where the potential V(x) and the nonlinearity g(x,u) are allowed to be sign-changing. Under some suitable assumptions on V and g, we obtain the multiplicity of solutions by using minimax methods.

Keywords

• Quasilinear Schrodinger equation
• symmetric mountain pass theorem
• Cerami condition