Critical gauged Schr\"{o}dinger equations in R^2 with vanishing potentials

TL;DR

This paper investigates a class of gauged nonlinear Schr"{o}dinger equations in two dimensions, establishing the existence of multiple solutions using variational methods, including the Mountain-Pass theorem and Ekeland's principle.

Contribution

The study introduces new existence results for solutions of gauged Schr"{o}dinger equations in R^2, including infinitely many solutions for odd nonlinearities.

Findings

Existence of two nontrivial solutions via variational methods.

Existence of infinitely many solutions for odd nonlinearities.

Application of Mountain-Pass theorem and Ekeland's variational principle.

Abstract

We study a class of gauged nonlinear Schr\"{o}dinger equations in the plane. We obtain existence of two nontrivial solutions via the Mountain-Pass theorem and Ekeland's variational principle. Moreover, we prove existence of infinitely many solutions for odd nonlinearities.