Existence and concentration of solution for a class of fractional elliptic equation in ${\mathbb{R}}^N$ via penalization method

Abstract

In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation $$ ε^{2s} (-Δ)^{s}{u}+V(z)u=f(u)\,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, $$ where $\epsilon$ is a positive parameter, $f$ has a subcritical growth, $V$ possesses a local minimum, $N>2s,$ $s\in (0,1),$ and $(-\Delta {)}^{s}u$ is the fractional laplacian.

References in corpus (1)

• Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity