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  • Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials
    Zhang, Xia ; Zhang, Binlin ; Repovš, Dušan, 1954-
    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.
    Source: Nonlinear Analysis. Theory, Methods and Applications. - ISSN 0362-546X (Vol. 142, 2016, str. 48-68)
    Type of material - article, component part ; adult, serious
    Publish date - 2016
    Language - english
    COBISS.SI-ID - 17674585

    Link(s):

    http://dx.doi.org/10.1016/j.na.2016.04.012
    Repository of the University of Ljubljana – RUL

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