Existence And Multiplicity Of Solutions To A New Class Of Variable Exponential Kirchhoff Equations

In this paper,the existence and multiplicity of solutions of Kirchhoff type problems with variable exponents are studied by using Ekeland's variational principle,mountain pass lemma and symmetric mountain pass lemma.On the one hand,we consider the following p(x)-Kirchhoff equations where ?(?)RN is a smooth bounded domain with boundary (?)?,a?b>0 are constants,p ? C(?)with 10,By applying the mountain pass lemma and the Ekeland's variational principle,it is proved that equation(0.1)has at least two nontrivial solutions.On the other hand,we consider the following p(x)-Kirchhoff fractional equations where ?(?)RN is a smooth bounded domain with boundary ??,a?b>0 are constants,??2,s ?(0,1),p:?×??(1,?)with 1