Existence and multiplicity results for a new $p(x)$-Kirchhoff problem

Hamdani, Mohamed Karim (avtor), Harrabi, Abdellaziz (avtor), Mtiri, Foued (avtor), Repovš, Dušan (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: variable exponent, nonlocal Kirchhoff equation, p(x)-Laplacian operator, Palais-Smale condition, Mountain Pass theorem, Fountain theorem
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2020
• Št. strani: art. 111598 ( 15 str.)
• Številčenje: Vol. 190
• PID: 20.500.12556/RUL-109278
• UDK: 517.956
• ISSN pri članku: 0362-546X
• DOI: 10.1016/j.na.2019.111598
• COBISS.SI-ID: 18706265
• Datum objave v RUL: 29.08.2019

HAMDANI, Mohamed Karim, HARRABI, Abdellaziz, MTIRI, Foued in REPOVŠ, Dušan, 2020, Existence and multiplicity results for a new ▫$p(x)$▫-Kirchhoff problem. Nonlinear Analysis [na spletu]. 2020. Vol. 190. [Dostopano 30 junij 2025]. DOI 10.1016/j.na.2019.111598. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=109278

Gradivo je del revije

• Naslov: Nonlinear Analysis
• Skrajšan naslov: Nonlinear anal.
• Založnik: Pergamon Press
• ISSN: 0362-546X
• COBISS.SI-ID: 26027520