Banach空间非线性混合型微分-积分方程非局部终值问题解的存在性

数学物理学报 ›› 2013, Vol. 33 ›› Issue (3): 550-560.

Banach空间非线性混合型微分-积分方程非局部终值问题解的存在性

谢胜利|戈慈水

安徽建筑工业学院数理系合肥 |230601

收稿日期:2011-10-12 修回日期:2012-12-10 出版日期:2013-06-25 发布日期:2013-06-25
基金资助:
安徽省自然科学基金(11040606M01)和安徽省教育厅自然科学重点基金(KJ2011Z057, KJ2011A061)资助

Existence of Solutions of Nonlocal Terminal Value Problems for Nonlinear Mixed Integro-Differential Equations in Banach Spaces

XIE Sheng-Li, GE Ci-Shui

Department of Mathematics &|Physics, Anhui University of Architecture, |Hefei 230601

Received:2011-10-12 Revised:2012-12-10 Online:2013-06-25 Published:2013-06-25
Supported by:
安徽省自然科学基金(11040606M01)和安徽省教育厅自然科学重点基金(KJ2011Z057, KJ2011A061)资助

摘要/Abstract

摘要：

使用M\"{o}nch不动点定理, 证明Banach空间非线性混合型微分-积分方程非局部终值问题解的存在性. 非紧性测度估计的限制性条件没有被使用, 其结果改进和推广了郭伟^[12]中相应的结果.

关键词: Volterra-Fredholm型微分-积分方程, 非局部终值问题, 不动点, Banach空间

Abstract:

Using M\"{o}nch fixed point theorem, this article proves the existence of solution of nonlocal terminal value problems
for first order nonlinear mixed integro-differential equations in Banach spaces, the restricted conditions on noncompactness measure estimation hasn't used and our result generalizes and improves the corresponding result
of Guo Wei [Guo Wei. A generalization and application of Ascoli--Arzela theorem. Journal of Systems Science and Mathematical Sciences (in Chinese), 2002, 22(1): 115--122].

Key words: Volterra-Fredholm integro-differential equation, Nonlocal terminal value problem, Fixed point, Banach spaces

中图分类号:

34G20

谢胜利, 戈慈水. Banach空间非线性混合型微分-积分方程非局部终值问题解的存在性[J]. 数学物理学报, 2013, 33(3): 550-560.

XIE Sheng-Li, GE Ci-Shui. Existence of Solutions of Nonlocal Terminal Value Problems for Nonlinear Mixed Integro-Differential Equations in Banach Spaces[J]. Acta mathematica scientia,Series A, 2013, 33(3): 550-560.

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