@Article{Figueiredo2020,
author = "Figueiredo, Giovany M. and Rădulescu, Vicenţiu D.",
title = "Nonhomogeneous equations with critical exponential growth and lack of compactness",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "1",
pages = "71--92",
doi = "https://doi.org/10.7494/OpMath.2020.40.1.71",
url = "https://doi.org/10.7494/OpMath.2020.40.1.71",
abstract = "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.",
keywords = "exponential critical growth, quasilinear equation, Trudinger-Moser inequality, Moser iteration",
issn = "1232-9274"
}