Soliton solutions for a class of generalized quasilinear Schrödinger equations

Abstract

In this paper, critical point theory is used to show the existence of nontrivial solutions for a class of generalized quasilinear Schrödinger equations $ \begin{equation*} -\Delta_pu-{|u|}^{\sigma-2}uh'({|u|}^\sigma)\Delta_ph({|u|}^\sigma) = f(x,u) \end{equation*} $ in a smooth bounded domain $ \Omega\subset{\mathbb{R}}^N $ with Dirichlet boundary conditions. Our result covers some typical physical models.

Keywords

• soliton solution
• quasilinear schrödinger equation
• critical point theory
• change of variables