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 - <p style="text-align: justify;">In this paper, we study the existence of &quot;weak solution&quot; 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 &quot;weak solution&quot; of this
problem.</p>