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.
(-\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.
| Original language | English |
|---|---|
| Pages (from-to) | 201-216 |
| Journal | Le Matematiche: journal of pure and applied mathematics |
| Volume | 68 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 7 May 2013 |
| Externally published | Yes |