Existence and iteration of positive solution for a multi-point boundary value problem with a $p$-Laplacian operator

De-Xiang Ma; Xue-Gang Chen

doi:10.4171/pm/1799

JournalspmVol. 65, No. 1pp. 67–80

Existence and iteration of positive solution for a multi-point boundary value problem with a $p$ -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:

{Φ p (u^{'}))^{'} + q (t) f (t, u) = 0, 0 < t < 1, u (0) = \sum_{i = 1}^{q - 1} γ + i u (δ_{i}), u (1) = \sum_{i = 1}^{m - 1} η_{i} u (ξ_{i}) .

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 $p$ -Laplacian operator. Port. Math. 65 (2008), no. 1, pp. 67–80

DOI 10.4171/PM/1799