Existence and iteration of positive solution for a multi-point boundary value problem with a <var>p</var>-Laplacian operator

Abstract

In this paper we obtain the existence of a positive solution and establish a corresponding iterative scheme for the following boundary value problem:

(Φp(u'))' + q(t) f(t,u) = 0,  0 < t < 1,

u(0) = ∑i=1,…,q−1 γiu(δi),  u(1)= ∑i=1,…,m−1 ηiu(ξi).

The main tool is the monotone iterative technique. Here the coefficient q(t) may be singular at t = 0,1.