无穷时滞一阶脉冲积分微分方程温和解的存在性

王永龙，李郅鸿

(兰州交通大学数理学院，甘肃兰州 730070)

无穷时滞一阶脉冲积分微分方程温和解的存在性

王永龙，李郅鸿

(兰州交通大学数理学院，甘肃兰州 730070)

利用预解算子理论，结合不动点定理，证明了无穷时滞一阶脉冲积分微分方程温和解的存在性.

积分微分方程；无穷时滞；不动点；预解算子；温和解

具有脉冲条件的泛函微分方程在许多领域中已被广泛应用，对其存在性结果的研究也取得了一些较好的成果[1-8]．本文主要考虑如下定义的具有无穷时滞的一阶脉冲积分微分方程温和解的存在性：

1 预备知识

设C(J,X)是由从J到X的所有连续泛函组成的Banach空间，其上范数定义为：) (X L是由从X到自身的有界线性算子组成的Banach空间．一个可测泛函是Bochner可积当且仅当是Lebesgue可积，L1(J,X)是由所有Bochner可积函数

2 主要结果

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[3] Chang Y K, Anguraj A, Karthikeyan K. Existence for impulsive neutral integrodifferential inclusions with nonlocal conditions via fractional operators [J]. Nonlinear Anal TMA, 2009, DOI: 10.1016/j.na.2009.02.121.

[4] Chang Y K, Anguraj A, Arjunan M M. Existence results for non-densely defined neutral differential inclusions with nonlocal conditions [J]. J Appl Math Comput, 2008, 28: 79-91.

[5] Hernandez E. Existence results for partial neutral integrodifferential equations with unbounded delay [J]. J Math Anal Appl, 2004, 292(1): 194-210.

[6] Li W S, Chang Y K, Nieto J J. Solvability of impulsive neutral evolution differential inclusions with state-dependent delay [J]. Math Comput Modelling, 2009, 49: 1920-1927.

[7] Liang J, Liu J H, Xiao T J. Nonlocal impulsive problems for integrodifferential equations [J]. Dyn Contin Discrete Impuls Syst, 2008, 15: 815-824.

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[9] Desch W, Grimmer R, Schappacher W. Some consideration for linear integrodifferential equations [J]. J Math Anal Appl, 1984, 104: 219-234.

Existence of M ild Solutions for First Order Impulsive Integrodifferential Equations with Infinite Delay

WANG Yonglong, LI Zhihong
(Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, China 730070)

Based upon theories of resolvent operator and fixed point theorem, existence of mild solutions for first order impulsive integrodifferential equations w ith infinite delay is proved.

Integrodifferential Equation; Infinite Delay; Fixed Point; Resolvent Operator; Mild Solution

O175.22

：A

：1674-3563(2014)03-0024-05

10.3875/j.issn.1674-3563.2014.03.004 本文的PDF文件可以从xuebao.wzu.edu.cn获得

(编辑：王一芳)

2013-11-04

王永龙(1989- )，男，甘肃兰州人，硕士研究生，研究方向：运筹学与控制论