Existence and multiplicity of positive solutions for a class of p ( x ) -Kirchhoff type equations

[摘要] In this article, we study the existence and multiplicity of positive solutions for the Neumann boundary value problems involving the p(x)-Kirchhoff of the form-M∫Ω1p(x)(∇up(x)+λup(x))dx(div(∇up(x)-2∇u)-λup(x)-2u)=f(x,u)inΩ,∂u∂v=0on∂Ω.Using the sub-supersolution method and the variational method, under appropriate assumptions on f and M, we prove that there exists λ* > 0 such that the problem has at least two positive solutions if λ > λ*, at least one positive solution if λ = λ* and no positive solution if λ < λ*. To prove these results we establish a special strong comparison principle for the Neumann problem. 2000 Mathematical Subject Classification: 35D05; 35D10; 35J60.

[学科分类] 数学（综合）

[关键词] p(x)-Kirchhoff;positive solution;sub-supersolution method;comparison principle