Existence and multiplicity of positive solutions for a class of p(x)-Kirchhoff type equations
Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China
Boundary Value Problems 2012, 2012:16 doi:10.1186/1687-2770-2012-16Published: 13 February 2012
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
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.