一类非线性三阶三点边值问题单调正解的存在性

Existence of Monotone Positive Solution for a Class of Nonlinear Third-Order Three-Point Boundary Value Problem

考虑了一类非线性三阶常微分方程三点边值问题单调正解的存在性.通过运用迭代技巧,不仅得到其单调正解的存在性,还给出两个迭代序列,并且迭代序列的初值是简单的零函数和一次函数,从计算的角度来说是有用的和可行的.最后通过实例说明了所得结果的重要性.

This paper is concerned with the existence of monotone positive solutions for three-point boundary value problem of a class of nonlinear third-order ordinary differential equation. By applying iterative techniques, the existence of monotone positive solution is obtained and two iterative sequences of monotone positive solution are given. Moreover, the iterative scheme starts off with zero function or linear function, which is very useful and feasible for computational purpose. At last, an example is also included to illustrate the importance of the results obtained.