Soliton solutions for a class of quasilinear Schrödinger equations with a parameter

Abstract

Using variational methods combined with perturbation arguments, we study the existence of nontrivial classical solution for the quasilinear Schrödinger equation \begin{equation*}\label{1.1} -Δu+ V(x)u+ \fracκ{2}[Δ|u|^2]u=l(u),\ x\in\mathbb{R}^N, \end{equation*} where $V:{\mathbb{R}}^N\to \mathbb{R}$ and $l:\mathbb{R}\to \mathbb{R}$ are continuous function, $\kappa$ is a parameter and $N\ge 3$. This model has been proposed in plasma physics and nonlinear optics. As a main novelty with respect to some previous results, we are able to deal with the case $\kappa >0$.

References in corpus (1)

• Electrons on Hexagonal lattices and applications to nanotubes