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

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.