Quasilinear elliptic problem in anisotrpic Orlicz-Sobolev space on unbounded domain

2022/09/22 by Wroński, Karol
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.10999

Abstract

We study a quasilinear elliptic problem -div (∇ Φ(∇ u))+V(x)N'(u)=f(u) with anisotropic convex function Φ on whole ℝⁿ. To prove existence of a nontrivial weak solution we use mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space W¹ L^Φ(ℝⁿ). As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden the class of considered functions Φ so our result generalizes earlier analogous results proved in isotropic setting.

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