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  • Supercritical fractional Kirchhoff type problems
    Ambrosio, Vincenzo, 1986- ; Servadei, Raffaella, 1973-
    In this paper we deal with the following fractional Kirchhoff problem ▫$$\begin{cases} \left[ \left( \iint_{\mathbb{R} \times \mathbb{R}} \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}dxdy \right) \right]^{p-1} ... (-\Delta)^s_p u = f(x,u) + \lambda|u|^{r-2}u & \text{in} \quad \Omega, \\ u=0 & \text{in} \quad \mathbb{R}^n\Omega, \end{cases}$$▫ Here ▫$\Omega \subset \mathbb{R}^n$▫ is a smooth bounded open set with continuous boundary ▫$\partial \Omega$▫, ▫$p \in (1, +\infty)$▫, ▫$s \in (0, 1)$▫, ▫$n > sp$▫, ▫$(-\Delta)^s_p$▫ is the fractional ▫$p$▫-Laplacian, ▫$M$▫ is a Kirchhoff function, ▫$f$▫ is a continuous function with subcritical growth, ▫$\lambda$▫ is a nonnegative parameter and ▫$r > p^\ast_s$▫, where ▫$p^\ast_s=\frac{np}{n-sp}$▫ is the fractional critical Sobolev exponent. By combining variational techniques and a truncation argument, we prove two existence results for this problem, provided that the parameter ▫$\lambda$▫ is sufficiently small.
    Vir: Fractional Calculus & Applied Analysis. - ISSN 1311-0454 (Vol. 22, iss. 5, 2019, str. 1351-1377)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18881625

    Povezava(-e):

    https://doi.org/10.1515/fca-2019-0071
    DOI

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