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

Author

Serena Dipierro, Giampiero Palatucci, and Enrico Valdinoci

Subjects
Nonlinear problems, fractional Laplacian, fractional Sobolev spaces, critical Sobolev exponent, spherical solutions, ground states, Mathematics, QA1-939
Abstract

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.

Published
2013

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