Existence of Nontrivial Solutions and High Energy Solutions for a Class of Quasilinear Schrödinger Equations via the Dual-Perturbation Method

Abstract

We study the quasilinear Schrödinger equation of the form $-\Delta u+V\left(x\right)u-\Delta \left(u^2\right)u=h\left(x,u\right)$, $x\in R^N$. Under appropriate assumptions on $V\left(x\right)$ and $h\left(x,u\right)$, existence results of nontrivial solutions and high energy solutions are obtained by the dual-perturbation method.