Existence of Weak Solution for $p(x)$-Kirchhoff Type Problem Involving the $p(x)$-Laplacian-like Operator by Topological Degree
Year: 2023
Author: Chakir Allalou, Mohamed El Ouaarabi, Said Melliani, Chakir Allalou, Said Melliani
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 2 : pp. 203–219
Abstract
In this paper, we study the existence of "weak solution" for a class of $p(x)$-Kirchhoff type problem involving the $p(x)$-Laplacian-like operator depending on two real parameters with Neumann boundary condition. Using a topological degree for a class of demicontinuous operator of generalized $(S_+)$ type and the theory of the variable exponent Sobolev space, we establish the existence of "weak solution" of this problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n2.5
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 2 : pp. 203–219
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: $p(x)$-Kirchhoff type problem $p(x)$-Laplacian-like operator weak solution topological degree methods variable exponent Sobolev space.