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∑−2i=1u∆(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.