Green’s Function for Periodic Solutions in Alternately Advanced and Delayed Differential Systems

被引：0
作者：
Kuo-Shou Chiu
机构：
[1] Universidad Metropolitana de Ciencias de la Educación,Departamento de Matemática, Facultad de Ciencias Básicas
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2020年 / 36卷
关键词：
piecewise constant arguments; Green’s function; periodic solutions; hybrid equations; fixed point theorems; 34A36; 34B27; 34K13; 37C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we investigate the existence of the periodic solutions of a nonlinear differential equation with a general piecewise constant argument, in short DEPCAG, that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use the Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results.
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页码：936 / 951
页数：15
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