00985nas a2200133   4500008004100000245010200041210006900143260002600212520042000238100002100658700002500679700002200704856012500726       2013                        en  d00aExistence and symmetry results for a Schrodinger type problem  involving the fractional Laplacian0 aExistence and symmetry results for a Schrodinger type problem in  bUniversity of Catania3 a<p>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 $s=1$.</p>1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico  uhttps://math.sissa.it/publication/existence-and-symmetry-results-schrodinger-type-problem-involving-fractional-laplacian