On asymptotic behavior of solutions to non-uniformly elliptic equations with generalized Orlicz growth

TL;DR

This paper investigates the long-term behavior of solutions to non-uniformly elliptic equations with generalized Orlicz growth, establishing Harnack inequalities and advancing understanding for (p,q) nonlinearities.

Contribution

It introduces new results on asymptotic behavior and Harnack inequalities for equations with nonstandard growth, especially in (p,q) and Orlicz settings.

Findings

Proved Harnack type inequalities for solutions.

Established asymptotic behavior results for non-uniformly elliptic equations.

Extended analysis to generalized Orlicz growth and (p,q) nonlinearities.

Abstract

We study asymptotic behavior of sub-solutions to non-uniformly elliptic equations with nonstandard growth. In particular, Harnack type inequalities are proved. Our approach gives new results for the cases with (p,q) nonlinearity and generalized Orlicz growth.