Existence of solutions for a class of \(p(x)\)-Kirchhoff type equation with dependence on the gradient. (English) Zbl 1422.35048

Summary: The object of this work is to study the existence of solutions for a class of \(p(x)\)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of \((S_+)\) type in the framework of variable exponent Sobolev spaces.


35J60 Nonlinear elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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