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Volume 36, Issue 2
Existence of Weak Solution for $p(x)$-Kirchhoff Type Problem Involving the $p(x)$-Laplacian-like Operator by Topological Degree

Mohamed El Ouaarabi, Chakir Allalou & Said Melliani

DOI: 10.4208/jpde.v36.n2.5

J. Part. Diff. Eq., 36 (2023), pp. 203-219.

Published online: 2023-06

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  • 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.

  • Keywords

$p(x)$-Kirchhoff type problem, $p(x)$-Laplacian-like operator, weak solution, topological degree methods, variable exponent Sobolev space.

  • AMS Subject Headings

35J66, 35J93, 35D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-203, author = {Ouaarabi , Mohamed ElAllalou , Chakir and Melliani , Said}, title = {Existence of Weak Solution for $p(x)$-Kirchhoff Type Problem Involving the $p(x)$-Laplacian-like Operator by Topological Degree}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {2}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n2.5}, url = {http://global-sci.org/intro/article_detail/jpde/21829.html} }
TY - JOUR T1 - Existence of Weak Solution for $p(x)$-Kirchhoff Type Problem Involving the $p(x)$-Laplacian-like Operator by Topological Degree AU - Ouaarabi , Mohamed El AU - Allalou , Chakir AU - Melliani , Said JO - Journal of Partial Differential Equations VL - 2 SP - 203 EP - 219 PY - 2023 DA - 2023/06 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n2.5 UR - https://global-sci.org/intro/article_detail/jpde/21829.html KW - $p(x)$-Kirchhoff type problem, $p(x)$-Laplacian-like operator, weak solution, topological degree methods, variable exponent Sobolev space. AB -

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.

Ouaarabi , Mohamed ElAllalou , Chakir and Melliani , Said. (2023). Existence of Weak Solution for $p(x)$-Kirchhoff Type Problem Involving the $p(x)$-Laplacian-like Operator by Topological Degree. Journal of Partial Differential Equations. 36 (2). 203-219. doi:10.4208/jpde.v36.n2.5
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