Existence of Positive Solution for a System of Quasilinear Schrodinger

TL;DR

This paper proves the existence of positive standing wave solutions for quasilinear Schrödinger systems using advanced variational methods and penalization techniques, overcoming non-differentiability challenges.

Contribution

It introduces a novel application of penalization and dual approaches to establish solutions for quasilinear Schrödinger systems, addressing non-differentiability issues.

Findings

Existence of positive solutions established.

Method successfully handles non-differentiability.

Refinements improve solution existence proofs.

Abstract

We investigate the existence of standing wave solutions for quasilinear Schrodinger systems. To address the challenges posed by non differentiability, we adopt the dual approach introduced by Colin and Jeanjean. The existence of solutions is established using Del Pino and Felmer's penalization technique, with refinements inspired by Alves' arguments.