Existence and multiplicity results for a new ▫$p(x)$▫-Kirchhoff problem
Hamdani, Mohamed Karim (Author), Harrabi, Abdellaziz (Author), Mtiri, Foued (Author), Repovš, Dušan (Author)

Abstract
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.

Language: English variable exponent, nonlocal Kirchhoff equation, p(x)-Laplacian operator, Palais-Smale condition, Mountain Pass theorem, Fountain theorem Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2020 art. 111598 ( 15 str.) Vol. 190 517.956 0362-546X 10.1016/j.na.2019.111598 18706265 305 230 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

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Title: Nonlinear Analysis Nonlinear anal. Pergamon Press 0362-546X 26027520