TY - JOUR T1 - Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian JF - Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -

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 $s=1$.

PB - University of Catania U1 - 7318 U2 - Mathematics U4 - -1 ER -