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  • Existence and multiplicity results for a new ▫$p(x)$▫-Kirchhoff problem
    Hamdani, Mohamed Karim ...
    In this work, we study the existence and multiplicity results for the following nonlocal-Kirchhoff problem: ▫$$\begin{cases} -\big(a-b \int_\Omega \frac{1}{p(x}|\nabla u|^{p(x)} dx \big) \; ... \text{div} (|\nabla u|^{p(x)-2} \nabla u) = \\ = \lambda |u|^{p(x)-2}u + g(x,u) & \text{in} \; \Omega \\ u=0 & \text{on} \; \partial \Omega \end{cases}$$▫ where ▫$a \ge b > 0$▫ are constants, ▫$\Omega \subset \mathbb{R}^N$▫ is a bounded smooth domain ▫$p \in C(\overline{\Omega})$▫, with ▫$N > p(x) > 1$▫, ▫$\lambda$▫ is a real parameter and ▫$g$▫ is a continuous function. The analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties.
    Source: Nonlinear Analysis. Theory, Methods and Applications. - ISSN 0362-546X (Vol. 190, Jan. 2020, art. 111598 ( 15 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2020
    Language - english
    COBISS.SI-ID - 18706265

    Link(s):

    https://doi.org/10.1016/j.na.2019.111598
    Repository of the University of Ljubljana – RUL
    DOI

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