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  • A critical fractional Choquard-Kirchhoff problem with magnetic field
    Xiang, Mingqi ; Rǎdulescu, Vicenţiu, 1958- ; Zhang, Binlin
    In this paper, we are interested in a fractional Choquard-Kirchhoff-type problem involving an external magnetic potential and a critical nonlinearity ▫$$M(\Vert u\Vert_{s,A}^2)[(-\Delta)_A^s u+u] = ... \lambda \int_{\mathbb{R}}^N\frac{F(|u|^2)}{|x-y|^\alpha} dy f(|u|^2)u + |u|^{2_s^\ast-2}u \quad \text{in} \quad \mathbb{R}^N,$$▫ ▫$$\Vert u\Vert_{s,A} = \left( \iint_{\mathbb{R}^{2N}} \frac {|u(x) - e^{i(x-y) \cdot A(\frac{x+y}{2})} u(y)|^2}{|x-y^{|N+2s}}dxdy+ \int_{\mathbb{R}^N} |u|^2 dx \right)^{1/2},$$▫ where ▫$N>2s$▫ with ▫$0<s<1$▫, ▫$M$▫ is the Kirchhoff function, ▫$A$▫ is the magnetic potential, ▫$(-\Delta)_A^s$▫ is the fractional magnetic operator, ▫$f$▫ is a continuous function, ▫$F(|u|) = \int_0^{|u|}f(t)dt$▫, ▫$\lambda > 0$▫ is a parameter, ▫$0 < \alpha < \min \{N,4s\}$▫ and ▫$2_s^\ast = \frac{2N}{N-2s}$▫ is the critical exponent of fractional Sobolev space. We first establish a fractional version of the concentration-compactness principle with magnetic field. Then, together with the mountain pass theorem, we obtain the existence of nontrivial radial solutions for the above problem in non-degenerate and degenerate cases.
    Vir: Communications in contemporary mathematics. - ISSN 0219-1997 (Vol. 21, no. 4, June 2019, art. 1850004 (36 str.))
    Vrsta gradiva - članek, sestavni del
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18361689

    Povezava(-e):

    https://doi.org/10.1142/S0219199718500049
    DOI

vir: Communications in contemporary mathematics. - ISSN 0219-1997 (Vol. 21, no. 4, June 2019, art. 1850004 (36 str.))

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