Nonhomogeneous equations with critical exponential growth and lack of compactness

Opuscula Mathematica

article

Giovany M. Figueiredo¹  Vicenţiu D. Rădulescu (corresponding author)² 

[1] Universidade de Brasília - UnB, Departamento de Matemàtica;"Simion Stoilow" Institute of Mathematics of the Romanian Academy

关键词: exponential critical growth;    quasilinear equation;    Trudinger-Moser inequality;    Moser iteration.;   

DOI  :  10.7494/OpMath.2020.40.1.71

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

We study the existence and multiplicity of positive solutions for the following class of quasilinear problems \[-\operatorname{div}(a(|\nabla u|^{p})| \nabla u|^{p-2}\nabla u)+V(\epsilon x)b(|u|^{p})|u|^{p-2}u=f(u) \qquad\text{ in } \mathbb{R}^N,\] where \(\epsilon\) is a positive parameter. We assume that \(V:\mathbb{R}^N \to \mathbb{R}\) is a continuous potential and \(f:\mathbb{R}\to\mathbb{R}\) is a smooth reaction term with critical exponential growth.

【 授权许可】

CC BY-NC