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.