On Analytic Periodic Solutions to Nonlinear Differential Equations With Delay (Advance)

被引：2
作者：
Kosov A.A. [1 ]
Semenov E.I. [1 ]
机构：
[1] Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, ul. Lermontova 134, Irkutsk
来源：
Russian Mathematics | 2018年 / 62卷 / 10期
基金：
俄罗斯基础研究基金会;
关键词：
differential equation with delay (advance); exact solution; first integral; Jacobi elliptic function; periodic solution; reaction–diffusion system; reduction to ODE system;
D O I：
10.3103/S1066369X18100043
中图分类号：
学科分类号：
摘要：
We study a system of the reaction–diffusion type, where diffusion coefficients depend in an arbitrary way on spatial variables and concentrations, while reactions are expressed as homogeneous functions whose coefficients depend in a special way on spatial variables. We prove that the system has a family of exact solutions that are expressed through solutions to a system of ordinary differential equations (ODE) with homogeneous functions in right-hand sides. For a special case of theODE systemwe construct a general solution represented by Jacobi higher transcendental functions. We also prove that these periodic solutions are analytic functions that can be expressed near each point on the period by convergent power series. © 2018, Allerton Press, Inc.
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页码：30 / 36
页数：6
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