%0 Journal Article %J Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %D 2013 %T Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian %A Serena Dipierro %A Giampiero Palatucci %A Enrico Valdinoci %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 $s=1$.

%B Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %I University of Catania %G en %1 7318 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T16:07:36Z No. of bitstreams: 1 1202.0576v1.pdf: 219939 bytes, checksum: 822c73753d6d4194cf48cb0ff9ad0e48 (MD5)