Existence, multiplicity and infinite solvability of positive solutions for p-Laplacian dynamic equations on time scales

Abstract

In this paper, by using Guo-Krasnosel'skii fixed point theorem in cones, we study the existence, multiplicity and infinite solvability of positive solutions for the following three-point boundary value problems for p-Laplacian dynamic equations on time scales [Φp(uΔ(t))]∇ + α(t)ƒ(t, u(t)) = 0, t ∈ [0, T]T, u(0) - B0(uΔ(η)) = 0, uΔ(T) = 0. By multiplicity we mean the existence of arbitrary number of solutions.