Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain

Karol Wroński

doi:10.1007/s10231-024-01477-5

Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain

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 the whole $\R^n$. To prove existence of a nontrivial weak solution we use the mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space $\WLPhispace(\R^n)$. 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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Author (1)

Karol Wroński dr inż.

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Keywords

ANISOTROPIC ORLICZ-SOBOLEV SPACE, VARIATIONAL VETHODS, LIONS LEMMA

Details

Category:

Articles

Type:

artykuły w czasopismach dostępnych w wersji elektronicznej [także online]

Published in:

ANNALI DI MATEMATICA PURA ED APPLICATA
ISSN: 0373-3114

Language:

English

Publication year:

2024

Bibliographic description:

Wroński K., Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain, ANNALI DI MATEMATICA PURA ED APPLICATA, 2024,10.1007/s10231-024-01477-5

DOI: