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Existence and multiplicity results for a new ▫$p(x)$▫Kirchhoff problem
Hamdani, Mohamed Karim
(
Author
),
Harrabi, Abdellaziz
(
Author
),
Mtiri, Foued
(
Author
),
Repovš, Dušan
(
Author
)
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Abstract
In this work, we study the existence and multiplicity results for the following nonlocalKirchhoff problem: ▫$$\begin{cases} \big(ab \int_\Omega \frac{1}{p(x}\nabla u^{p(x)} dx \big) \; \text{div} (\nabla u^{p(x)2} \nabla u) = \\ = \lambda u^{p(x)2}u + g(x,u) & \text{in} \; \Omega \\ u=0 & \text{on} \; \partial \Omega \end{cases}$$▫ 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
Keywords:
variable exponent
,
nonlocal Kirchhoff equation
,
p(x)Laplacian operator
,
PalaisSmale condition
,
Mountain Pass theorem
,
Fountain theorem
Work type:
Article (dk_c)
Tipology:
1.01  Original Scientific Article
Organization:
PEF  Faculty of Education
Year:
2020
Number of pages:
art. 111598 ( 15 str.)
Numbering:
Vol. 190
UDC:
517.956
ISSN on article:
0362546X
DOI:
10.1016/j.na.2019.111598
COBISS.SIID:
18706265
Views:
305
Downloads:
230
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Record is a part of a journal
Title:
Nonlinear Analysis
Shortened title:
Nonlinear anal.
Publisher:
Pergamon Press
ISSN:
0362546X
COBISS.SIID:
26027520
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