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arXiv · 2209.10999

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

Karol Wroński
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Abstract

We study a quasilinear elliptic problem $-\text{div} (\nabla \Phi(\nabla u))+V(x)N'(u)=f(u)$ with anisotropic convex function $\Phi$ on whole $\mathbb{R}^n$. To prove existence of a nontrivial weak solution we use mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space $W^1 L^{\Phi}(\mathbb{R}^n)$. As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden the class of considered functions $\Phi$ so our result generalizes earlier analogous results proved in isotropic setting.

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Karol Wroński. 2022-09-22. Quasilinear elliptic problem in anisotrpic Orlicz-Sobolev space on unbounded domain. https://arxiv.org/abs/2209.10999

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