This paper deals with the following class of nonlocal Schr\"odinger equations $$(-\Delta)s u + u = u^{p-1}u \ \ \text{in} \ \mathbb{R}N, \quad \text{for} \ s\in (0,1).$$ 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 $s=1$.
Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian / Serena, Dipierro; Palatucci, Giampiero; Enrico, Valdinoci. - In: LE MATEMATICHE. - ISSN 0373-3505. - 68:1(2013), pp. 201-216. [10.4418/2013.68.1.15]
Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
PALATUCCI, Giampiero;
2013-01-01
Abstract
This paper deals with the following class of nonlocal Schr\"odinger equations $$(-\Delta)s u + u = u^{p-1}u \ \ \text{in} \ \mathbb{R}N, \quad \text{for} \ s\in (0,1).$$ 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 $s=1$.File | Dimensione | Formato | |
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