Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials

Xia Zhang (Author), Binlin Zhang (Author), Dušan Repovš (Author)

Abstract

This paper is concerned with the following fractional Schrödinger equations involving critical exponents: ▫$$(-\Delta)^\alpha u + V(x)u = k(x)f(u) + \lambda|u|^{2_\alpha^\ast-2}u \quad \text{in} \; \mathbb{R}^N,$$▫ where ▫$(-\Delta)^\alpha$▫ is the fractional Laplacian operator with ▫$\alpha \in (0,1)$▫, ▫$N \ge 2$▫, ▫$\lambda$▫ is a positive real parameter and ▫$2_\alpha^\ast = 2N/(N-2\alpha)$▫ is the critical Sobolev exponent, ▫$V(x)$▫ and ▫$k(x)$▫ are positive and bounded functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space and the minimax arguments, we obtain the existence of a nontrivial radially symmetric weak solution for the above-mentioned equations without assuming the Ambrosetti-Rabinowitz condition on the subcritical nonlinearity.

Keywords

fractional Schrödinger equations;critical Sobolev exponent;Ambrosetti-Rabinowitz condition;concentration compactness principle;

Data

Language:	English
Year of publishing:	2016
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.95
COBISS:	17674585
ISSN:	0362-546X
Views:	515
Downloads:	349
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 48-68
Issue:	ǂVol. ǂ142
Chronology:	2016
DOI:	http://dx.doi.org/10.1016/j.na.2016.04.012
ID:	11233020