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

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

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.

• Jezik: Angleški jezik
• Ključne besede: fractional Schrödinger equations, critical Sobolev exponent, Ambrosetti-Rabinowitz condition, concentration compactness principle
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2016
• Št. strani: Str. 48-68
• Številčenje: Vol. 142
• PID: 20.500.12556/RUL-111174
• UDK: 517.95
• ISSN pri članku: 0362-546X
• DOI: http://dx.doi.org/10.1016/j.na.2016.04.012
• COBISS.SI-ID: 17674585
• Datum objave v RUL: 25.09.2019

Gradivo je del revije

• Naslov: Nonlinear Analysis
• Skrajšan naslov: Nonlinear anal.
• Založnik: Pergamon Press
• ISSN: 0362-546X
• COBISS.SI-ID: 26027520