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

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

Keywords

variable exponent;nonlocal Kirchhoff equation;p(x)-Laplacian operator;Palais-Smale condition;Mountain Pass theorem;Fountain theorem;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	18706265
ISSN:	0362-546X
Views:	523
Downloads:	339
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. 111598 ( 15 str.)
Issue:	ǂVol. ǂ190
Chronology:	Jan. 2020
DOI:	10.1016/j.na.2019.111598
ID:	11210442