Multiple solutions for a quasilinear Schrödinger equation on ${\mathbb{R}}^N$}

Abstract

The multiplicity of positive weak solutions for a quasilinear Schrödinger equations $-L_{p}u+(\lambda A(x)+1)|u{|}^{p-2}u=h(u)$ in ${\mathbb{R}}^N$ is established, where $L_{p}u\doteq {\epsilon }^p{\Delta }_{p}u+{\epsilon }^p{\Delta }_p(u^2)u$, $A$ 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.

arXiv admin note: substantial text overlap with arXiv:1304.4960