Boundary Value Problems
Volume 2009 (2009), Article ID 685040, 6 pages
doi:10.1155/2009/685040

Existence of positive solution to second-order three-point BVPs on time scales

Abstract

We are concerned with the following nonlinear second-order three-point boundary value problem on time scales −xΔΔ(t)=f(t,x(t)), t∈[a,b]𝕋, x(a)=0, x(σ2(b))=δx(η), where a,b∈𝕋 with a<b,    η∈(a,b)𝕋 and 0<δ<(σ2(b)−a)/(η−a). A new representation of Green's function for the corresponding linear boundary value problem is obtained and some existence criteria of at least one positive solution for the above nonlinear boundary value problem are established by using the iterative method.