Nonlocal impulsive problems for nonlinear differential equations in Banach spaces

被引：113
作者：
Liang, Jin [2 ,3 ]
Liu, James H. [1 ,4 ]
Xiao, Ti-Jun [5 ]
机构：
[1] James Madison Univ, Dept Math, Harrisonburg, VA 22807 USA
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
[3] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China
[4] Anhui Univ, Hefei, Anhui, Peoples R China
[5] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2009年 / 49卷 / 3-4期
基金：
中国国家自然科学基金;
关键词：
Nonlocal and impulsive conditions; SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS; EVOLUTION-EQUATIONS; CAUCHY-PROBLEMS; EXISTENCE; UNIQUENESS; SYSTEMS;
D O I：
10.1016/j.mcm.2008.05.046
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions u'(t) = Au(t) + f(t, u(t)), 0 <= t <= K, t not equal t(i), u(0) + g(u) = u(0), Delta u(t(i)) = I-i(u(t(i))), i = 1,2,...,p, 0 < t(1) < t(2) < (...) < t(p) < K, by combining and extending some earlier work on equations with nonlocal conditions and equations with impulsive conditions. Here, A is the generator of a strongly continuous semigroup in a Banach space, g constitutes a nonlocal condition, and Delta u(t(i)) = u(t(i)(+)) - u(t(i)(-)) constitutes an impulsive condition. New results are obtained. (c) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：798 / 804
页数：7
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