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

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

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2016
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	517.95
COBISS:	17674585
ISSN:	0362-546X
Št. ogledov:	515
Št. prenosov:	349
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 48-68
Zvezek:	ǂVol. ǂ142
Čas izdaje:	2016
DOI:	http://dx.doi.org/10.1016/j.na.2016.04.012
ID:	11233020