TY  - JOUR
ID  - Figueiredo2020
LB  - Figueiredo2020
AU  - Figueiredo, Giovany M.
AU  - Rădulescu, Vicenţiu D.
TI  - Nonhomogeneous equations with critical exponential growth and lack of compactness
ST  - Nonhomogeneous equations with critical exponential growth and lack of compactness
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 1
SP  - 71
EP  - 92
DO  - https://doi.org/10.7494/OpMath.2020.40.1.71
UR  - https://doi.org/10.7494/OpMath.2020.40.1.71
AB  - 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.
KW  - exponential critical growth
KW  - quasilinear equation
KW  - Trudinger-Moser inequality
KW  - Moser iteration
SN  - 1232-9274
ER  -