Work

Anisotropic quasilinear elliptic systems with homogeneous critical nonlinearities

Year: 2025

Type: article

Abstract: In 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.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.12008

Author: Mathew Gluck

Institution: Southern Illinois University Carbondale

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: LEAPS-MPS: Failure of Compactness in Elliptic Problems with Applications in Science and Mathematics