Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
Keywords:
Nonlinear problems, fractional Laplacian, fractional Sobolev spaces, critical Sobolev exponent, spherical solutions, ground statesAbstract
This paper deals with the following class of nonlocal Schrödinger 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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