茹靜,裴明鶴

(1.北華大學(xué)數(shù)學(xué)學(xué)院,吉林吉林 132013;2.吉林化工學(xué)院數(shù)理系,吉林吉林 132022)

高階微分積分方程的單調(diào)迭代法及其應(yīng)用

茹靜1,2,裴明鶴1

(1.北華大學(xué)數(shù)學(xué)學(xué)院,吉林吉林 132013;2.吉林化工學(xué)院數(shù)理系,吉林吉林 132022)

首先利用上下解方法以及微分不等式理論給出了n階微分積分方程的初值問題解的存在性及其單調(diào)迭代法,然后將所得結(jié)果應(yīng)用到n階微分方程的兩點(diǎn)邊值問題,得到了n階非線性兩點(diǎn)邊值問題解的存在性及其單調(diào)迭代法,所得結(jié)果推廣了已有的結(jié)果.

初值問題；邊值問題；單調(diào)迭代法

1 引言

眾所周知,利用上下解研究邊值問題解的存在性及其單調(diào)迭代法是求邊值問題近似解的非常行之有效的方法之一.關(guān)于一階和二階邊值問題的單調(diào)迭代法,已有很多結(jié)果[13],但關(guān)于高階邊值問題的單調(diào)迭代法在文獻(xiàn)上卻較少見到[48],究其原因主要是因?yàn)闃?gòu)造單調(diào)迭代序列通常需要依賴微分不等式,而高階微分不等式是較難解決的課題,從而給用上下解方法研究邊值問題的單調(diào)迭代法帶來了較大的困難.

本文主要研究n階微分積分方程的初值問題

的兩點(diǎn)邊值問題解的存在性及其單調(diào)迭代法.本文所得關(guān)于邊值問題(簡稱BVP)(1.3),(1.4)的解的存在性及其單調(diào)迭代法將文[4]的相應(yīng)結(jié)果作為特例.

2 n階微分積分方程初值問題的單調(diào)迭代法

3 n階微分方程兩點(diǎn)邊值問題的單調(diào)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.

茹靜(1978-),碩士,研究方向：微分方程邊值問題.

2000M SC:34B15