This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data of the following form − a + b Ω 1 p(x) |∇u| p(x) dx div |∇u| p(x)−2 ∇u = f (x, u) , in Ω u = 0 on ∂Ω , where Ω is a smooth open subset of R N and p ∈ C(Ω) with N < p − = inf x∈Ω p(x) ≤ p + = sup x∈Ω p(x) < +∞, a, b are positive constants and f : Ω × R → R is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.

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Abstract. In this paper we obtain existence results of k distinct pairs nontrivial solutions for an impulsive boundary value problem of p(t)-Kirchhoff type under certain conditions on the parameter λ.

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