Banach空间中二阶非线性混合型积分-微分方程初值问题的解

J4 ›› 2010, Vol. 45 ›› Issue (12): 93-97.

Banach空间中二阶非线性混合型积分-微分方程初值问题的解

李耀红^1,2,张海燕¹

1. 宿州学院数学系, 安徽宿州 234000; 2. 山东大学数学学院, 山东济南 250100

收稿日期:2009-10-30 出版日期:2010-12-16 发布日期:2011-03-16
作者简介:李耀红(1978-),男,讲师,硕士,研究方向为非线性泛函分析. Email:liz.zhanghy@163.com
基金资助:
安徽省教育厅自然科学研究资助项目(KJ2010B226);宿州学院自然科学基金资助项目(2009yzk17)

The solutions of initial value problems for nonlinear second order integro-differential equations of mixed type in Banach spaces

LI Yao-hong^1,2, ZHANG Hai-yan¹

1. Department of Mathematics, Suzhou University, Suzhou 234000, Anhui, China;
2. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2009-10-30 Online:2010-12-16 Published:2011-03-16

摘要/Abstract

摘要：

得到了一个新的比较结果,利用该结果和Mnch不动点定理,获得了Banach空间中二阶非线性混合型积分-微分方程解的存在性定理,同时还利用非紧性测度给出了存在最小最大解的一个充分条件,改进和推广了已有的结果。

关键词: 积分-微分方程;初值问题;比较结果;非紧性测度

Abstract:

By using a new established comparison result and the Mnch fixed point theorem, the existence of solutions of initial value problems for nonlinear second order intergro-differential equations of mixed type in Banach spaces is investigated. Also, one sufficient condition for the existence of minimal and maximal solutions is obtained through applying the measure of noncompactness. The results improve and generalize some well-known results.

Key words: integro-differential equations; initial value problems; comparison result; measure of noncompactness

李耀红1,2,张海燕1. Banach空间中二阶非线性混合型积分-微分方程初值问题的解[J]. J4, 2010, 45(12): 93-97.

LI Yao-hong1,2, ZHANG Hai-yan1. The solutions of initial value problems for nonlinear second order integro-differential equations of mixed type in Banach spaces[J]. J4, 2010, 45(12): 93-97.

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