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

### De-Xiang Ma

North China Electric Power University, Beijing, China### Xue-Gang Chen

North China Electric Power University, Beijing, China

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## 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.

## Cite this article

De-Xiang Ma, Xue-Gang Chen, Existence and iteration of positive solution for a multi-point boundary value problem with a <var>p</var>-Laplacian operator. Port. Math. 65 (2008), no. 1, pp. 67–80

DOI 10.4171/PM/1799