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

Le Matematiche

关键词: Nonlinear problems;    fractional Laplacian;    fractional Sobolev spaces;    critical Sobolev exponent;    spherical solutions;    ground states;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown