Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian

This paper deals with the following class of nonlocal Schrodinger equations (-\Delta)^s u +  u =  |u|^{p-1}u   in  \mathbb{R}^N,  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.

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