Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales

In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales(φp(uΔ(t)))Δ+h(t)f(uσ(t))=0,t∈[a,b],u(a)−B0(uΔ(a))=0,uΔ(σ(b))=0, where φp(u)φp(u) is p  -Laplacian operator, i.e., φp(u)=|u|p−2uφp(u)=|u|p−2u, p>1p>1. Some new results are obtained for the existence of at least single, twin or triple positive solutions of the above problem by using Krasnosel'skii's fixed point theorem, new fixed point theorem due to Avery and Henderson and Leggett–Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian boundary value problems on time scales has been studied.