Ground state solutions for nonlinear fractional Schr\"{o}dinger equations in $\mathbb{R}^N$

TL;DR

This paper develops a variational method to find ground state solutions for nonlinear fractional Schrödinger equations in multi-dimensional space, expanding the understanding of fractional quantum systems.

Contribution

Introduces a variational approach based on minimization on the Nehari manifold to construct solutions for fractional Schrödinger equations, a novel application in this context.

Findings

Successfully constructs ground state solutions for fractional Schrödinger equations.

Demonstrates the effectiveness of the variational method in this setting.

Provides a framework for future studies on fractional quantum equations.

Abstract

We construct solutions to a class of Schr\"{o}dinger equations involving the fractional laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.