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Existence of solutions for a \(p(x)\)-Kirchhoff-type equation. (English) Zbl 1172.35401

Summary: This paper is concerned with the existence and multiplicity of solutions to a class of \(p(x)\)-Kirchhoff-type problem with Dirichlet boundary data. By means of a direct variational approach and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence and multiplicity of solutions for the problem.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J20 Variational methods for second-order elliptic equations
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