On a class fractional Schr\"odinger equations with indefinite potential involving critical exponential growth

TL;DR

This paper proves the existence and multiplicity of weak solutions for a class of fractional Schrödinger equations with indefinite potentials and critical exponential growth nonlinearities, using variational methods.

Contribution

It introduces new existence and multiplicity results for nonlocal fractional Schrödinger equations with indefinite potentials and critical exponential nonlinearities.

Findings

Existence of weak solutions established

Multiple solutions demonstrated using variational methods

Applicable to equations with sign-changing potentials

Abstract

It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The proofs of our existence results rely on minimization methods in combination with the mountain-pass theorem.