On a p(x)- Kirchhoff fourth order problem involving Leray-Lions type operators

摘要

The aim of this work is to study the existence and the multiplicity of nontrivial weak solutions for a class of p(x)-Kirchhoff type problems involving Leray-Lions type operators and a changing sign weight under no flux boundary condition. By using the mountain pass type theorem and the Ekeland's variational principle, we obtain at least two nontrivial weak solutions; moreover, by following the steps described by the Fountain Theorem, we will find an infinitely many weak solutions.