Solutions and Green’s functions for some linear second-order three-point boundary value problems

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Abstract

In this paper we consider the Green’s functions for a second-order linear ordinary differential equation with some three-point boundary conditions. We give exact expressions of the unique solutions for the linear three-point boundary problems by the Green’s functions. As applications, we study the iterative solutions for some nonlinear singular second-order three-point boundary value problems.

Keywords

Green’s function
Second-order differential equation
Three-point boundary value problem
Explicit solution
Iterative solution

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Research supported by the National Natural Science Foundation of China (10471075), the Natural Science Foundation of Shandong Province of China (Y2006A04) and the Doctoral Program Foundation of Education Ministry of China (20060446001).