Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space

In this paper, we study existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems $$-{\mathrm{\Delta }}_{\mathrm{\Phi }}u+V(ϵx)\varphi (\mathrm{\mid }u\mathrm{\mid })u=f(u)in{\mathbb{R}}^N(N\ge 2),$$ where $\mathrm{\Phi }(t)={\int }_0^{\mathrm{\mid }t\mathrm{\mid }}\varphi (s)sds$ is a N-function, ${\mathrm{\Delta }}_{\mathrm{\Phi }}$ is the $\mathrm{\Phi }$-Laplacian operator, $ϵ$ is a positive parameter, $V:{\mathbb{R}}^N\to \mathbb{R}$ is a continuous function and $f:\mathbb{R}\to \mathbb{R}$ is a $C^1$-function.