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

• Main Authors: Claudianor O. Alves, Ailton R. da Silva
• Format: Article
• Language: English
• Published: Texas State University 2016-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Variational method; quasilinear problem, Orlicz-Sobolev space
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/158/abstr.html

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 $N\geq 2$.