This paper is concerned with the existence and multiplicity of weak solutions for a p(x)-Kirchho type problem of the following form 8< : M Z 1 p(x) jujp(x) dx (jujp(x)2u) = f(x; u) in u = u = 0 on @ ; by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle in two cases when the Caratheodory function f(x; u) having special structure.
