Anisotropic quasilinear elliptic systems with homogeneous critical nonlinearities

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 14 Apr 2025Embargo end date: 01 Jan 2023 English Publisher:WileyJournal:Mathematische Nachrichten, volume 298, pages 1,633-1,662 (issn: 0025-584X, eissn: 1522-2616,

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Authors: Gluck, Mathew;

doi: 10.1002/mana.12008 , 10.48550/arxiv.2312.17737

arXiv: 2312.17737

Anisotropic quasilinear elliptic systems with homogeneous critical nonlinearities

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Abstract

AbstractIn this work, we consider a system of quasilinear elliptic equations driven by an anisotropic ‐Laplacian. The lower order nonlinearities are in potential form and exhibit critical Sobolev growth. We exhibit conditions on the coefficients of the differential operator, the domain of the unknown function, and the lower order nonlinearities under which nontrivial solutions are guaranteed to exist and conditions on these objects under which a nontrivial solution does not exist.

Related Organizations

Southern Illinois University Carbondale
United States

Keywords

Mathematics - Analysis of PDEs, quasilinear elliptic equation, non-existence, existence, FOS: Mathematics, Existence problems for PDEs: global existence, local existence, non-existence, 35J47 (Primary) 35J62, 35J50 (Secondary), Quasilinear elliptic equations with \(p\)-Laplacian, \(p\)-Laplacian, Analysis of PDEs (math.AP)

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