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  • Existence of solutions for a bi-nonlocal fractional ▫$p$▫-Kirchhoff type problem
    Xiang, Mingqi ; Zhang, Binlin ; Rǎdulescu, Vicenţiu, 1958-
    In this paper, we are concerned with the existence of nonnegative solutions for a ▫$p$▫-Kirchhoff type problem driven by a non-local integro-differential operator with homogeneous Dirichlet boundary ... data. As a particular case, we study the following problem ▫$$\begin{cases} M(x,[u]^p_{s,p})(-\Delta)_p^su = f(x,u,[u]^p_{s,p}) & \text{in} \quad \Omega\\ u=0 & \text{in} \quad \mathbb{R}^N \setminus \Omega, \\ [u]^p_{s,p} = \iint_{\mathbb{R}^{2N}} \frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy, \end{cases}$$▫ where ▫$(-\Delta)_p^s$▫ is a fractional ▫$p$▫-Laplace operator, ▫$\Omega$▫ is an open bounded subset of ▫$\mathbb{R}^N$▫ with Lipschitz boundary, View the ▫$M \colon \Omega \times \mathbb{R}_0^+ \to \mathbb{R}^+$▫ is a continuous function and ▫$f \colon \Omega \times \mathbb{R} \times \mathbb{R}_0^+ \to \mathbb{R}$▫ is a continuous function satisfying the Ambrosetti-Rabinowitz type condition. The existence of nonnegative solutions is obtained by using the Mountain Pass Theorem and an iterative scheme. The main feature of this paper lies in the fact that the Kirchhoff function ▫$M$▫ depends on ▫$x \in \Omega$▫ and the nonlinearity ▫$f$▫ depends on the energy of solutions.
    Source: Computers & mathematics with applications. - ISSN 0898-1221 (Vol. 71, iss. 1, 2016, str. 255-266)
    Type of material - article, component part
    Publish date - 2016
    Language - english
    COBISS.SI-ID - 17568857

    Link(s):

    http://dx.doi.org/10.1016/j.camwa.2015.11.017

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