Existence and multiplicity results for a new ▫$p(x)$▫-Kirchhoff problemHamdani, Mohamed Karim (Avtor) Harrabi, Abdellaziz (Avtor) Mtiri, Foued (Avtor) Repovš, Dušan (Avtor) variable exponentnonlocal Kirchhoff equationp(x)-Laplacian operatorPalais-Smale conditionMountain Pass theoremFountain theoremIn 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.20202019-08-29 08:19:09Članek v reviji109278sl