Existence and concentration of positive solutions for a class of discontinuous quasilinear Schrödinger problems in R N $\mathbb{R}^{N}$

Abstract

Abstract In this paper, a class of quasilinear Schrödinger equations with discontinuous nonlinearity is considered. After changing variables, by using nonsmooth critical point theory, we obtain the existence and concentration of positive solutions for this problem under suitable conditions. Our results cover and extend some results for these differentiable quasilinear Schrödinger problems.

Keywords

• Quasilinear Schrödinger equation
• Variational method
• Discontinuous nonlinearity
• Positive solution