同时带有强迫项和有限时滞的Lienard方程周期解的存在性
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摘要
利用Mawhin延拓定理证明了一类具有强迫项的有限时滞Lienard方程x″(t)+f_1(x)x′(t)+f_2(x)(x′(t))~2+g(x(t-τ))=e(t)存在周期解的充分条件.
In this paper,we use the Mawhin's continuity theorem to establish and prove new results on the sufficient conditions of the periodic solution of existence for a class forced and finite delayed Lienard equations of the form x"(t) + f_1(x)x'(t) + f_2(x)(x'(t))~2+ g(x(t-τ)) = e(t)
In this paper,we use the Mawhin's continuity theorem to establish and prove new results on the sufficient conditions of the periodic solution of existence for a class forced and finite delayed Lienard equations of the form x"(t) + f_1(x)x'(t) + f_2(x)(x'(t))~2+ g(x(t-τ)) = e(t)
引文
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[9]陈仕洲.一类Lienard型p-Laplacian方程周期解的存在唯一性[J].数学的实践与认识,2013,43(8):244-253.
[10]陈月红.具有两个偏差变元的Lienard型方程周期解的存在性[J].数学的实践与认识,2014,44(18):315-320.
[11]Lasalle J P,and Lefschetz S.Stability by Liapunov's Direct Method with Application[M].New York:Academic Press,1961.
[12]Kuang Y.Delay Differential Equations with Applications in Population Dynamics[M].New York:Academic Press,1993.
[13]Yoshizawa T.Stability Theory and the Eristence of Periodic Solutions and Almost Periodic Solutions[M].New York:Springer-Verlag,1975.
[14]Zhang Zhi-fen,Li Cheng-zhi.Fundamentals of Bifurcation Theorey of Vertor Fields[M].Beijing:Beijing University Press,1997.(in Chinese).
[15]田德生.三阶常系数拟线性泛函微分方程的周期解[J].纯粹数学与应用数学,2013,29(3):233-240.
[16]黄勇,姚晓洁,秦发金.一类二阶微分方程周期解的存在性和唯一性[J],广西民族大学学报(自然科学版),2014,20(4):46-53.
[17]Chin Yuan-Shan,Liu Yong-qing.Stability of Dynamical Systems[M].Beijing:Science Press,1989.(in Chinese).
[18]陈新一.高阶非线性中立型泛函微分方程周期解的存在性[J].山东大学学报(理学版),2011,46(8):47-51.
[19]陈楷城.二阶非线性中立型泛函微分方程周期解的存在性[J].数学的实践与认识,2014,44(3):268-273.
[20]Liao Xiao-xin.Theory and Application of Stability for Dynamical Systems[M].Beijing:Defence Industrial Press,2000.(in Chinese).
[21]Chen Yu-shu,Tang Yun.Modern Analytic Methods in Nonlinear DynamicsfM].Beijing:Science Press.2002.(in Chinese).
[22]Gaines R E,and Mawhin J L.Coincidence Degree and Nonlinear Differential EquationsfMJ.LMN586,Berlin:Springer-Verlag,1977.
[23]Deimling K.Nonlinear functional analysis[M].Berlin:Springer-Verlag,1985.
[24]Omari P,Villari G,and Zanolin F.Periodic solutions of the Lienard equation with one-side growth restrictions[J].J Diff Equs,1987,67:278-293.
[2]Hale J K.Theory of Functional Differential Equations[M].New York:Springer-Verlag,1977.
[3]Nussbaum R D.Periodic solutions of some nonlinear autonomous functional differential equations[J].Ann Math Pure Appl,1974,10:263-306.
[4]魏俊杰,黄启昌,关于具有限时滞Lienard方程周期解的存在性[J].科学通报,1997,42(9):906-909.
[5]Conti R,and Sansone G.Nonlinear Differential Equations[M].London:Pergamon Press,1964.
[6]Hale J K.Introduction to Functional Differential Equations[M].Berlin:Springer-Verlag,1977.
[7]陈红斌,李开泰,李东升.Lienard方程周期解的存在唯一与唯二性问题[J].数学学报,2004,47(3):417-424.
[8]陈世哲,陈仕洲.具有两个偏差变元的Lienard型方程的周期解的存在唯一性[J].科技通报,2012,28(11):11-15.
[9]陈仕洲.一类Lienard型p-Laplacian方程周期解的存在唯一性[J].数学的实践与认识,2013,43(8):244-253.
[10]陈月红.具有两个偏差变元的Lienard型方程周期解的存在性[J].数学的实践与认识,2014,44(18):315-320.
[11]Lasalle J P,and Lefschetz S.Stability by Liapunov's Direct Method with Application[M].New York:Academic Press,1961.
[12]Kuang Y.Delay Differential Equations with Applications in Population Dynamics[M].New York:Academic Press,1993.
[13]Yoshizawa T.Stability Theory and the Eristence of Periodic Solutions and Almost Periodic Solutions[M].New York:Springer-Verlag,1975.
[14]Zhang Zhi-fen,Li Cheng-zhi.Fundamentals of Bifurcation Theorey of Vertor Fields[M].Beijing:Beijing University Press,1997.(in Chinese).
[15]田德生.三阶常系数拟线性泛函微分方程的周期解[J].纯粹数学与应用数学,2013,29(3):233-240.
[16]黄勇,姚晓洁,秦发金.一类二阶微分方程周期解的存在性和唯一性[J],广西民族大学学报(自然科学版),2014,20(4):46-53.
[17]Chin Yuan-Shan,Liu Yong-qing.Stability of Dynamical Systems[M].Beijing:Science Press,1989.(in Chinese).
[18]陈新一.高阶非线性中立型泛函微分方程周期解的存在性[J].山东大学学报(理学版),2011,46(8):47-51.
[19]陈楷城.二阶非线性中立型泛函微分方程周期解的存在性[J].数学的实践与认识,2014,44(3):268-273.
[20]Liao Xiao-xin.Theory and Application of Stability for Dynamical Systems[M].Beijing:Defence Industrial Press,2000.(in Chinese).
[21]Chen Yu-shu,Tang Yun.Modern Analytic Methods in Nonlinear DynamicsfM].Beijing:Science Press.2002.(in Chinese).
[22]Gaines R E,and Mawhin J L.Coincidence Degree and Nonlinear Differential EquationsfMJ.LMN586,Berlin:Springer-Verlag,1977.
[23]Deimling K.Nonlinear functional analysis[M].Berlin:Springer-Verlag,1985.
[24]Omari P,Villari G,and Zanolin F.Periodic solutions of the Lienard equation with one-side growth restrictions[J].J Diff Equs,1987,67:278-293.