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, (?p(u?(t)))? + ?h(t)f(u(t)) = 0, t ? [a, b]T’ u(a) ? u?(a) = m??2i=1u?(?i), u?(b) = 0, m ? 3, where ?p(u) = |u|p?2u, p > 1 and ? > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solutions and nonexistence are obtained for ? evaluated in different intervals by using Guo-Krasnosel’skii fixed point theorem.