Banach空间非线性脉冲Volterra积分方程组的整体解

基金项目: 国家自然科学基金资助重大项目(19990510);国家教委博士点专项基金资助项目(D09901)

Global Solutions of Systems of Nonlinear Impulsive Volterra Integral Equations in Banach Spaces

摘要: 研究Banach空间中定义在无穷区间R⁺上具有无穷多个脉冲点的非线性脉冲Volterra积分方程组解的存在性。给出了若干极值解的存在定理,改进了定义在有限区间上具有有限个脉冲点情形时该类方程的相应结果,并利用该结果讨论了一个无穷维积分方程组。
- 脉冲Volterra积分方程组 /
- Tonelli方法 /
- 极值解 /
- 锥和半序
Abstract: The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R⁺ with an infinite number of moments of impulse effect in Banach spaces is studied.Some existence theorems of extremal solutions are obtained,which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect.The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.
- system of impulsive Volterra integral equations /
- Tonelli.s method /
- extremal solutions /
- cone and partial ordering

[1]	Lakshimikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations[M]. Singapore: World Scientific,1 989.
[2]	GUO Da-jun. Nonlinear impulsive Volterra integral equations in Banach spaces and applications[J]. J Appl Math Stochastic Anal,1993,6(1):35-48.
[3]	GUO Da-jun, Lakshimikantham V. Nonlinear Problems in Abstract Cones[M]. Boston and New York: Academic Press Inc,1988.
[4]	GUO Da-jun. Impulsive integral equations in Banach spaces and applications[J]. J Appl Math Stochastic Anal,1992,5(2):111-1 22.
[5]	Martin R H. Nonlinear Operators and Differential Equations in Banach Space[M]. New York: J Wiley and Sons,1976.
[6]	Heinz H P. On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions[J]. Nonlinear Anal,1983,7(12):1351-1371.
[7]	GUO Da-jun. Extremal solutions of nonlinear Fredholm integral equations in Banach spaces[J]. Northeastern Math J,1991,7(4): 416-423.
[8]	Vaughn R L. Existence and comparison results for nonlinear Volterr a integral equations in a Banach space[J]. Appl Anal,1978,7(2):337-348.
[9]	CHEN Fang-qi. Existence of solutions for mixed monotone impulsive Volterra integral equations in Banach spaces[J]. Acta Math Scientia,1998, 18(4):371-378.
[10]	陈芳启. Banach空间混合单调脉冲微分积分方程解的存在性[J]. 系统科学与数学,1999,19(1):111-115.
[11]	Deimling K. Nonlinear Functional Analysis[M]. Berlin: Sprin ger-Verlag,1985.