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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.