Solvability of Second Order Delta-Nabla p-Laplacian m-point Eigenvalue Problem on Time Scales

Abstract

In this paper, we are concerned with the following eigenvalue problem of m-point boundary value problem for p-Laplacian dynamic equation on time scales, ϕp u ∆ t ∇ + λh t f u t = 0, t ∈ [a, b]T , u a − u ∆ a = m∑−2 i=1 u ∆ ξi , u ∆ b = 0, m ≥ 3, where ϕp u = |u| p−2u, p > 1 and λ > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solutions and nonexistence are obtained for λ evaluated in different intervals by using Guo-Krasnosel’skii fixed point theorem.