高階微分積分方程的單調迭代法及其應用

茹靜,裴明鶴

(1.北華大學數學學院,吉林吉林 132013;2.吉林化工學院數理系,吉林吉林 132022)

高階微分積分方程的單調迭代法及其應用

茹靜1,2,裴明鶴1

(1.北華大學數學學院,吉林吉林 132013;2.吉林化工學院數理系,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迭代法,然后將所得結果應用到n階微分方程的兩點邊值問題,得到了n階非線性兩點邊值問題解的存在性及其單調迭代法,所得結果推廣了已有的結果.

初值問題；邊值問題；單調迭代法

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.關于一階和二階邊值問題的單調迭代法,已有很多結果[13],但關于高階邊值問題的單調迭代法在文獻上卻較少見到[48],究其原因主要是因為構造單調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

的兩點邊值問題解的存在性及其單調迭代法.本文所得關于邊值問題(簡稱BVP)(1.3),(1.4)的解的存在性及其單調迭代法將文[4]的相應結果作為特例.

2 n階微分積分方程初值問題的單調迭代法

3 n階微分方程兩點邊值問題的單調迭代法

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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