The Liouville theorems for elliptic equations with nonstandard growth

TL;DR

This paper establishes Liouville-type theorems and nonexistence results for solutions of elliptic equations with nonstandard growth, broadening understanding of such equations in mathematical analysis.

Contribution

It introduces new Liouville theorems for -harmonic equations with nonstandard growth, expanding the theoretical framework for these complex PDEs.

Findings

Proved Liouville-type theorems for -harmonic equations

Established nonexistence results for certain classes of solutions

Provided illustrative examples demonstrating the theorems

Abstract

We study solutions and supersolutions of homogeneous and nonhomogeneous $\mathcal{A}$-harmonic equations with nonstandard growth in $\mathbb{R}^n$. Various Liouville-type theorems and nonexistence results are proved. The discussion is illustrated by a number of examples.