Ground states solutions for a non-linear equation involving a pseudo-relativistic Schr\"odinger operator

TL;DR

This paper establishes the existence, regularity, and symmetry of ground state solutions for a nonlinear equation involving a pseudo-relativistic Schrödinger operator in the entire space.

Contribution

It provides the first comprehensive analysis of ground states for this class of pseudo-relativistic operators, including their existence and symmetry properties.

Findings

Existence of ground state solutions proven.

Ground states exhibit regularity and symmetry.

Results applicable to a broad class of nonlinear equations.

Abstract

In this paper we prove the existence, regularity and symmetry of a ground state for a nonlinear equation in the whole space, involving a pseudo-relativistic Schr\"odinger operator.