Sign-changing solutions for a class of fractional Schr\"odinger equations with vanishing potentials

TL;DR

This paper establishes the existence of sign-changing solutions for a class of fractional Schrödinger equations with potentials that vanish at infinity, using variational methods and deformation techniques.

Contribution

It introduces a novel approach combining minimization and deformation lemmas to find sign-changing solutions in fractional Schrödinger equations with vanishing potentials.

Findings

Existence of sign-changing solutions proven.

Application of minimization and deformation methods.

Addresses equations with potentials vanishing at infinity.

Abstract

In this paper we consider a class of fractional Schr\"odinger equations with potentials vanishing at infinity. By using a minimization argument and a quantitative deformation Lemma, we prove the existence of a sign-changing solution.