Existence Of Solutions For A P(x)-Kirchhoff-type Equation

This paper is concerned with the existence and multiplicity solutions to a class of p(x)-Kirchhoff-type problem with Dirichlet boundary data.By means of the theory of the variable exponent Sobolev spaces W^1,p(x)(Ω) and the variational approaches such as Mountain pass lemma,fountain theorem,Dual fountain theorem,we establish conditions ensuring the existence and multiplicity of solutions for the problem.