Multiple positive solutions for p-Laplacian m-point boundary value problems on time scales

Let TT be a time scale such that 0,T∈T0,T∈T, ai ⩾ 0 for i = 1, …, m − 2. Let ξi satisfy 0 < ξ1 < ξ2 < ⋯ < ξm−2 < ρ(T  ) and ∑i=1m-2ai<1. We consider the following p-Laplacian m-point boundary value problem on time scales(ϕp(uΔ(t)))∇+a(t)f(t,u(t))=0,t∈(0,T),u(0)=0,ϕp(uΔ(T))=∑i=1m-2aiϕp(uΔ(ξi)),where a ∈ Cld ((0, T), [0, ∞)) and f ∈ Cld ((0, T) × [0, ∞), [0, ∞)). Some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems respectively. In particular, our criteria extend and improve some known results.