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, 2023)
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 tworeal parameters with Neumann boundary condition. Using a topological degree fora class of demicontinuous operator of generalized $(S_+)$ type and the theory of thevariable exponent Sobolev space, we establish the existence of "weak solution" of thisproblem.
Keywords: $p(x)$-Kirchhoff type problem; $p(x)$-Laplacian-like operator; weak solution; topological degree methods; variable exponent Sobolev space.