Banach空间Volterra型二阶脉冲积分-微分方程的初值

在无穷区间上,用半序方法讨论有无穷脉冲项的非线性二阶Volterra型脉冲积分-微分方程的初值问题。利用逐段求解法和数学归纳法,给出有无穷脉冲项的非线性二阶Volterra型脉冲积分-微分方程无穷区间上的解,得到了省去了对脉冲项的限制及非紧性测度的估计。利用无穷区间上的结论给出了有限区间上非线性二阶Volterra型脉冲积分-微分方程的解,并在特殊条件下给出几个推论。

Initial Value Problems for Second Drder Impulsive Integro-Differential Equation of Volterra Type in Banach Space

This paper uses the partial ordering method to study the existence of the solution for the second order nonlinear impulsive integro-differential equation of Volterra type on infinite interval with infinite impulsive times in Banach space.By introducing an interim space and using progressive estimation method,some restrictive conditions on impulsive terms are deleted.At the same time,the conclusion of the second order nonlinear impulsive integro-differential equation of Volterra type on finite interval are got by using the conclusions on infinite interval.Finally,several conclusions are got in special conditions.