Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations

TL;DR

This paper proves the existence, non-negativity, and radial symmetry (up to translation) of least energy solutions for a broad class of autonomous quasi-linear elliptic equations on R^n, advancing understanding of their fundamental properties.

Contribution

It establishes the existence and symmetry of least energy solutions for a general class of quasi-linear elliptic equations, extending previous results to broader conditions.

Findings

Least energy solutions exist for the class of equations studied.

All least energy solutions are non-negative.

Solutions are radially symmetric up to translation.

Abstract

For a general class of autonomous quasi-linear elliptic equations on R^n we prove the existence of a least energy solution and show that all least energy solutions do not change sign and are radially symmetric up to a translation in R^n.