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

Language: English fractional Schrödinger equations, critical Sobolev exponent, Ambrosetti-Rabinowitz condition, concentration compactness principle Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2016 str. 48-68 Vol. 142 517.95 0362-546X http://dx.doi.org/10.1016/j.na.2016.04.012 17674585 292 239 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

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Title: Nonlinear Analysis Nonlinear anal. Pergamon Press 0362-546X 26027520