Sublinear Impulse Effects and Solvability of Boundary Value Problems for Differential Equations with Impulses
Sublinear Impulse Effects and Solvability of Boundary Value Problems for Differential Equations with Impulses
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DOI：
10.1006/jmaa.2001.7548
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发表时间：
2001-12
影响因子：
1.3
通讯作者：
Dong Yujun
中科院分区：
文献类型：
--
作者：
Dong Yujun
脉冲微分方程出现在许多应用科学中。最近，脉冲微分方程理论的发展取得了长足的进展。但是为了将微分方程上的结果推广到脉冲情况，我们必须对脉冲效应施加一些限制，如单调性和有界性。本文假设脉冲效应是次线性或渐近线性的。在这些假设下，我们将二阶微分方程的Picard BVP和一阶微分方程的PBVP的一些基本结果推广到脉冲情况。在第3节中，我们考虑皮卡德BVP x q ft， x q ht, x s 0, 1.1 ŽŽŽ xt s I x x y 0, xt s J x x y 0, I s 1, 2，…， p， Ž。Ž。Ž。Ž。ŽŽ I I I I I I I I
Impulse differential equations have appeared in many of the applied wx sciences 2. Recently, development of the theory of impulsive differential wx equations has taken flight 14. But in order to generalize the results on differential equations to the impulse case we have to impose some restricwx tions 57 on the impulsive effects, such as monotonicity and boundedness. In this paper we assume that the impulsive effects are sublinear or asymptotically linear. Under these assumptions we generalize some basic results about the Picard BVP of second-order differential equations and PBVP of first-order differential equations to the impulsive case. In Section 3 we consider the Picard BVP x q ft, x q ht, x s 0, 1.1 ŽŽŽ xt s I xt y 0, xt s J xt y 0, i s 1, 2,..., p, Ž. Ž. Ž. Ž. ŽŽ i i i i i i