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

By Claudianor Oliveira Alves, Olimpio Hiroshi Miyagaki. 2015

160 citations recorded by the source corpus.

In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation $$ \epsilon^{2s} (-\Delta)^{s}{u}+V(z)u=f(u)\,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, $$ 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f149b8dc0b33766e11addbdcca3754ff75f2c469

Citations in the corpus

• The concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system (2017, unknown): “For the concentration phenomena around a local minimum of the potential V , see [2,21] for the subcritical and the critical cases, respectively.”