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

Abstract

In this paper, we study existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems \[ - Δ_Φu + V(εx)ϕ(\vert u\vert)u = f(u)\quad \mbox{in} \quad \mathbb{R}^{N} \,\,\, ( N\geq 2 ), \] where $\Phi (t)={\int }_0^{|t|}\varphi (s)sds$ is a N-function, ${\Delta }_{\Phi }$ is the $\Phi$-Laplacian operator, $\epsilon$ 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.

References in corpus (2)

• On a non-homogeneous eigenvalue problem involving a potential: an Orlicz-Sobolev space setting
• Multiple solutions for elliptic equations involving a general operator in divergence form