王永龍，李郅鴻

(蘭州交通大學(xué)數(shù)理學(xué)院，甘肅蘭州 730070)

無窮時滯一階脈沖積分微分方程溫和解的存在性

王永龍，李郅鴻

(蘭州交通大學(xué)數(shù)理學(xué)院，甘肅蘭州 730070)

利用預(yù)解算子理論，結(jié)合不動點定理，證明了無窮時滯一階脈沖積分微分方程溫和解的存在性.

積分微分方程；無窮時滯；不動點；預(yù)解算子；溫和解

具有脈沖條件的泛函微分方程在許多領(lǐng)域中已被廣泛應(yīng)用，對其存在性結(jié)果的研究也取得了一些較好的成果[1-8]．本文主要考慮如下定義的具有無窮時滯的一階脈沖積分微分方程溫和解的存在性：

1 預(yù)備知識

設(shè)C(J,X)是由從J到X的所有連續(xù)泛函組成的Banach空間，其上范數(shù)定義為：) (X L是由從X到自身的有界線性算子組成的Banach空間．一個可測泛函是Bochner可積當(dāng)且僅當(dāng)是Lebesgue可積，L1(J,X)是由所有Bochner可積函數(shù)

2 主要結(jié)果

[1] Anguraj A, Arjunan M M, Hernandez E. Existence results for an impulsive neutral functional differential equation with state-dependent delay [J]. Appl Anal, 2007, 86(7): 861-872.

[2] Chang Y K, Anguraj A, Arjunan M M. Existence results for impulsive neutral functional differential equations w ith infinite delay [J]. Nonlinear Anal HS, 2008, 2(1): 209-218.

[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.

[8] Liang J, Liu J H, Xiao T J. Nonlocal impulsive problems for nonlinear differential equations in Banach spaces [J]. Math Comput Model, 2009, 49: 798-804.

[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文件可以從xuebao.wzu.edu.cn獲得

(編輯：王一芳)

2013-11-04

王永龍(1989- )，男，甘肅蘭州人，碩士研究生，研究方向：運籌學(xué)與控制論