Periodic solutions and stability in a nonlinear neutral system of differential equations with infinite delay

被引：7
|
作者：
Mesmouli M.B. [1 ]
Ardjouni A. [1 ,2 ]
Djoudi A. [1 ]
机构：
[1] Applied Mathematics Lab, Department of Mathematics, Faculty of Sciences, University of Annaba, P.O. Box 12, Annaba
[2] Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras
来源：
Boletín de la Sociedad Matemática Mexicana | 2018年 / 24卷 / 1期
关键词：
Contraction; Floquet theory; Fundamental matrix solution; Integral equation; Krasnoselskii’s theorem; Neutral differential equation; Periodic solution;
D O I：
10.1007/s40590-016-0155-1
中图分类号：
学科分类号：
摘要：
In this paper, we study the existence of periodic solutions of the nonlinear neutral system of differential equations ddtx(t)=A(t)x(t)+ddtQ(t,x(t-g(t)))+∫-∞tD(t,s)F(x(s))ds.Using Krasnoselskii’s fixed point theorem, we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness of periodic solution and stability of the zero solution. Our results extend some earlier publications. © 2016, Sociedad Matemática Mexicana.
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页码：239 / 255
页数：16
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