Mathematica Eterna
Open Access

Abstract

Multiple positive solutions of a m-point p-Laplacian boundary value problem involving derivative on time scales

Baoling Li and Chengmin Hou

This paper is concerned with the existence of positive solutions to the p-Laplacian dynamic equation φp(u â–³∇(t))
∇ + h(t)f(t, u(t), uâ–³(t)) = 0, t ∈ [0, T]T, subject to boundary conditions u(0)−B0( Pm−2 i=1 αiu â–³(ξi)) = 0, u â–³(T) = 0, u â–³∇(0) = 0, where φp(u) = |u| p−2u with p > 1. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we prove the m-point boundary value problem has at least triple or arbitrary positive solutions. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting. An example illustrates the application of the results obtained