JournalspmVol. 65 / No. 1DOI 10.4171/pm/1799

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

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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.