Multiple Solutions for a Quasilinear Schrödinger Equation on $\mathbb{R}^{N}$

Abstract

The multiplicity of positive weak solutions is established for quasilinear Schrödinger equations −L p u+(λA(x)+1)|u| p−2 u=h(u) in $\mathbb{R}^{N}$ , where L p u=ϵ p Δ p u+ϵ p Δ p (u 2)u, A is a nonnegative continuous function and nonlinear term h has a subcritical growth. We achieved our results by using minimax methods and Lusternik-Schnirelman theory of critical points.