Asymptotic behavior of least energy solutions to the Finsler Lane-Emden problem with large exponents

TL;DR

This paper investigates the asymptotic behavior of least energy solutions to the Finsler Lane-Emden problem with large exponents, providing key formulae for understanding solutions in anisotropic settings.

Contribution

It introduces new asymptotic formulae for solutions to the Finsler Lane-Emden problem as the exponent grows large, extending analysis to anisotropic operators.

Findings

Derived asymptotic formulae for solutions at large exponents

Analyzed solutions driven by the Finsler N-Laplacian

Extended understanding of anisotropic Lane-Emden problems

Abstract

In this paper we are concerned with the least energy solutions to the Lane-Emden problem driven by an anisotropic operator, so-called the Finsler $N$-Laplacian, on a bounded domain in $\mathbb{R}^N$. We prove several asymptotic formulae as the nonlinear exponent gets large.