VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Fractional Choquard-Kirchhoff problems with critical nonlinearity and Hardy potential
    Chen, Wenjing ; Rǎdulescu, Vicenţiu, 1958- ; Zhang, Binlin
    In this paper, we investigate the following fractional p-Kirchhoff type problem ▫$$\begin{cases} \left( a+b[u]_{s,p}^{p(\theta -1)}\right) (-\Delta )^s_pu = \Big ({\mathcal {I}}_\mu *|u|^q\Big ... )|u|^{q-2}u+\frac{|u|^{p_{\alpha }^*-2}u}{|x|^\alpha },\ u>0, & \text{in}\; \Omega ,\\ u=0, \ &{} \text{in}\; {\mathbb{R}}^N \setminus \Omega , \end{cases}$$▫ where ▫$[u]_{s,p}^{p}=\displaystyle \iint _{{\mathbb {R}}^{2N}} \frac{|u(x) - u(y)|^{p}}{|x - y|^{N+ps}}\, dxdy$▫, ▫$\Omega $▫ is a bounded smooth domain of ▫${\mathbb {R}}^N$▫ containing 0 with Lipschitz boundary, ▫$(-\Delta )_{p}^{s}$▫ denotes the fractional p-Laplacian, ▫$0\le \alpha<ps<N$▫ with ▫$s\in (0,1)$▫, ▫$p>1$▫, ▫$a\ge 0$▫, ▫$b>0$▫, ▫$1<\theta \le p_\alpha ^*/ p$▫, ▫$p_\alpha ^*=\frac{(N-\alpha )p}{N-ps}$▫ is the fractional critical Hardy-Sobolev exponent, ▫${\mathcal {I}}_\mu (x)=|x|^{-\mu }$▫ is the Riesz potential of order ▫$\mu \in (0,\min \{N,2ps\})$▫, ▫$q\in (1, Np/(N-ps))$▫ satisfies some restrictions. By the concentration-compactness principle and mountain pass theorem, we obtain the existence of a positive weak solution for the above problem as q satisfies suitable ranges.
    Vir: Analysis and mathematical physics. - ISSN 1664-2368 (Vol. 11, iss. 3, Sep. 2021, art. 132 (25 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 69494019

    Povezava(-e):

    https://link.springer.com/article/10.1007/s13324-021-00564-7
    DOI

vir: Analysis and mathematical physics. - ISSN 1664-2368 (Vol. 11, iss. 3, Sep. 2021, art. 132 (25 str.))
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