on a p(x)-kirchhoff equation via variational methods

This paper is concerned with the existence of two nontrivial weak solutions for a p(x)-kirchhoff type problem of the following form ( −m  r ω 1 p(x) |∇u| p (x) dx ∆p(x)u = λ(x)|u| q(x)−2u in ω, u = 0 on ∂ω, by using the mountain pass theorem of ambrosetti and rabinowitz and ekeland’s variational principle and the theory of the variable exponent sobolev spaces.