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

Abstract

This paper deals with the following class of nonlocal Schrödinger equations $$(-\Delta {)}^{s}u+u=|u{|}^{p-1}u\text{in}{\mathbb{R}}^N,\text{for}s\in (0,1).$$ 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 $s=1$.

References in corpus (2)

• Uniqueness and Nondegeneracy of Ground States for $(-\Delta {)}^{s}Q+Q-Q^{\alpha +1}=0$ in $\mathbb{R}$
• The Pohozaev identity for the fractional Laplacian

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