高阶微分积分方程的单调迭代法及其应用

茹静,裴明鹤

(1.北华大学数学学院,吉林吉林 132013;2.吉林化工学院数理系,吉林吉林 132022)

高阶微分积分方程的单调迭代法及其应用

茹静1,2,裴明鹤1

(1.北华大学数学学院,吉林吉林 132013;2.吉林化工学院数理系,吉林吉林 132022)

首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果.

初值问题；边值问题；单调迭代法

1 引言

众所周知,利用上下解研究边值问题解的存在性及其单调迭代法是求边值问题近似解的非常行之有效的方法之一.关于一阶和二阶边值问题的单调迭代法,已有很多结果[13],但关于高阶边值问题的单调迭代法在文献上却较少见到[48],究其原因主要是因为构造单调迭代序列通常需要依赖微分不等式,而高阶微分不等式是较难解决的课题,从而给用上下解方法研究边值问题的单调迭代法带来了较大的困难.

本文主要研究n阶微分积分方程的初值问题

的两点边值问题解的存在性及其单调迭代法.本文所得关于边值问题(简称BVP)(1.3),(1.4)的解的存在性及其单调迭代法将文[4]的相应结果作为特例.

2 n阶微分积分方程初值问题的单调迭代法

3 n阶微分方程两点边值问题的单调迭代法

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Monotone iterative techn ique and itsapp lication for higher order itegral-differen tial equations

RU Jing1,2,PEIming-he1

(1.Mathematics College,Beihua University,Jilin 132013,China; 2.Departm ent of Mathem atics,Jilin Institute of Chem ical Technology,Jilin 132022,China)

In this paper,the existence and them onotone iterative technique of solutions of initial value problems for n th-order integral-differential equations are studied firstly by means of upper and lower solutions and differential inequality theory,then the obtained results are employed to dealwith the two-point boundary value problems for n th-order differentialequations,the existence and them onotone iterative technique of solutions for n th-order non linear two-point boundary value problems are obtained.Our results generalized the exist resu lts.

initial value problems,boundary value prob lem,m onotone iterative technique

O175.8

A

1008-5513(2009)02-0302-08

2007-02-04.

茹静(1978-),硕士,研究方向：微分方程边值问题.

2000M SC:34B15