mountain pass solution for a p(t)-biharmonickirchhoff-type equation

In this paper we deal with the existence of weak solution for a p(t)-kirchhoff type problem of the following formleft{begin{array}{ll}-left(a-b int_{omega}frac{1}{p(x)}|delta u|^{p(x)},dxright)delta(|delta u|^{p(x)-2}delta u)=lambda |u|^{p(x)-2}u+g(x,u) & text{ in } omega,u=delta u=0 & textrm{ on } partialomega.end{array}right.using the mountain pass theoem, we establish conditions ensuring the existence result.