%0 Journal Article
%T Existence and symmetry results for a Schr£żdinger type problem involving the fractional Laplacian
%A Serena Dipierro
%A Giampiero Palatucci
%A Enrico Valdinoci
%J Mathematics
%D 2012
%I arXiv
%X This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.
%U http://arxiv.org/abs/1202.0576v1