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Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials
Zhang, Xia (Author), Zhang, Binlin (Author), Repovš, Dušan (Author)

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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.

Language:English
Keywords:fractional Schrödinger equations, critical Sobolev exponent, Ambrosetti-Rabinowitz condition, concentration compactness principle
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2016
Number of pages:str. 48-68
Numbering:Vol. 142
UDC:517.95
ISSN on article:0362-546X
DOI:http://dx.doi.org/10.1016/j.na.2016.04.012 Link is opened in a new window
COBISS.SI-ID:17674585 Link is opened in a new window
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Record is a part of a journal

Title:Nonlinear Analysis
Shortened title:Nonlinear anal.
Publisher:Pergamon Press
ISSN:0362-546X
COBISS.SI-ID:26027520 This link opens in a new window

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