Electron. J. Diff. Equ., Vol. 2016 (2016), No. 158, pp. 1-24.

Multiplicity and concentration behavior of solutions for a quasilinear problem involving N-functions via penalization method

Claudianor O. Alves, Ailton R. da Silva

Abstract:
In this work we study the existence, multiplicity and concentration of positive solutions for the quasilinear problem
$$ - \Delta_{\Phi}u + V(\epsilon x)\phi(| u|)u = f(u)\quad \text{in } \mathbb{R}^N, $$
where $\Phi(t) = \int_0^{| t|}\phi(s)sds$ is an N-function, $\Delta_{\Phi}$ is the $\Phi$-Laplacian operator, $\epsilon$ is a positive parameter, and $N\geq 2$.

Submitted March 15, 2016. Published June 21, 2016.
Math Subject Classifications: 35A15, 35B40, 35J62, 46E30.
Key Words: Variational method; quasilinear problem, Orlicz-Sobolev space.

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Claudianor O. Alves
Universidade Federal de Campina Grande
Unidade Acadêmica de Matemática - UAMat
CEP: 58.429-900 - Campina Grande - PB, Brazil
email: coalves@dme.ufcg.edu.br
Ailton R. da Silva
Universidade Federal de Campina Grande
Unidade Acadêmica de Matemática - UAMat
CEP: 58.429-900 - Campina Grande - PB, Brazil
email: ardsmat@gmail.com

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