| 非线性微分方程的正周期解 |
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| 引用本文： | 刘玉记,葛渭高.非线性微分方程的正周期解[J].高校应用数学学报(英文版),2003,18(4):373-382. |
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| 作者姓名： | 刘玉记 葛渭高 |
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| 作者单位： | Liu Yuji Ge Weigao1 Dept. of Math.，Yueyang Teacher's Univ.，Yueyang 414000，China. 2 Dept. of Appl. Math.，Beijing Institute of Technology，Beijing 100081，China. |
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| 基金项目： | The first author was supported by the Science Foundation of Educational Committee of HunanProvince ( 99C0 1 ) and the second author by the National Natural Science Foundation of China ( 1 9871 0 0 5 ) |
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| 摘 要： | § 1 IntroductionIn1 ] ,Saker and Agarwal studied the existence and uniqueness of positive periodicsolutions of the nonlinear differential equationN′(t) =-δ(t) N(t) + p(t) N(t) e- a N(t) ,(1 )whereδ(t) and p(t) are positive T-periodic functions.They proved that if p* >δ* ,then(1 ) has a unique T-periodic positive solution,wherep* =min0≤ t≤ Tp(t) ,δ* =max0≤ t≤ Tδ(t) . In view ofthe papermentioned above,whatcan be said aboutequation(1 ) when p* ≤δ* ?In this paper,we conside…
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Positive periodic solutions of nonlinear differential equations |
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| Liu Yuji,Ge Weigao.Positive periodic solutions of nonlinear differential equations[J].Applied Mathematics A Journal of Chinese Universities,2003,18(4):373-382. |
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| Authors: | Liu Yuji Ge Weigao |
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| Institution: | (1) Dept. of Math., Yueyang Teacher’s Univ., 414000 Yueyang, China;(2) Dept. of Appl. Math., Beijing Institute of Technology, 100081 Beijing, China |
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| Abstract: | The nonlinear differential equation x′(t)=-δ(t)x(t)+f(t,x(t))(*) is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t .It is showed that (*) has at leasttwo positive T -periodic solutions under certain growth conditions imposed on f .Applications will be presented to illustrate the main results. |
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| Keywords: | positive periodic solution differential equation fixed-point theorem growth condition |
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