一类脉冲种群模型渐近概周期解的研究
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摘要
基于Mawhin延拓定理,研究了一类脉冲种群模型严格正的渐近概周期解的存在性。所得结论推广了已有文献的结论。由于Mawhin延拓定理之前仅被用来证明很多类方程(如:脉冲微分方程、泛函微分方程、积分方程、Lienard型方程、P-Laplacian方程等)周期解或概周期解的存在性,故具一定的创新性。
Based on the Mawhin continuous theorem,the existence of strictly positive asymptotically almost periodic solutions of a class of impulsive population models is studied. The conclusion generalizes the conclusion of the existing literatures. Since the Mawhin continuous theorem is only used to prove the existence of periodic solutions or almost periodic solutions of equations(for example: impulsive differential equation,functional differential equation,integral equation,Lienard equation,P-Laplacian equation),the main result is innovative.
Based on the Mawhin continuous theorem,the existence of strictly positive asymptotically almost periodic solutions of a class of impulsive population models is studied. The conclusion generalizes the conclusion of the existing literatures. Since the Mawhin continuous theorem is only used to prove the existence of periodic solutions or almost periodic solutions of equations(for example: impulsive differential equation,functional differential equation,integral equation,Lienard equation,P-Laplacian equation),the main result is innovative.
引文
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[2]Bainov D D,Simeonov P S.Impulsive Differential Equations:Periodic Solutionand Applica-Tions[M].Longman,London,UK,1993
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[4]李建利.脉冲微分方程边值问题和周期解[D].长沙:湖南大学,2006Li Jianli.Boundary Value Problems and Periodic Solutions of Impulsive Differential Equations[D].Changsha,Hunan University,2006(in Chinese)
[5]傅金波,陈兰荪.基于生态环境和反馈控制的多种群竞争系统的正周期解[J].数学物理学报,2017,37(3):553-561Fu Jinbo,Chen Lansun.Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls[J].Acta Mathematica Scientia,2017,37(3):553-561(in Chinese)
[6]黄勇,黄燕革.具有强迫项的有限时滞Lienard方程周期解的存在性[J].四川师范大学学报:自然科学版,2016,39(1):111-116Huang Yong,Huang Yange.The Existence of Periodic Solutions for a Class of Forced and Finite Delayed Lienard Equations[J].Journal of Sichuan Normal University:Natural Science,2016,39(1):111-116(in Chinese)
[7]汪小明.一类具多个偏差变元Rayleigh型p-Laplacian方程周期解[J].数学研究,2012,5(2):115-123Wang Xiaoming.Periodic Solutions to a Kind of Rayleigh Type P-Laplacian Equation with Deviating Arguments[J].Journal of Mathematical Study,2012,5(2):115-123(in Chinese)
[8]Xie Y,Li X.Almost Periodic Solutions of Single Population Model with Hereditary Effects[J].Appl Math Comput,2008,203(2):690-697
[9]Alzabut J O,Stamov G T,Sermutlu E.Positive Almost Periodic Solutions for a Delay Logarith-Mic Population Model[J].Mathematical and Computer Modelling,2011,53(1):161-167
[10]Wang L,Yu M.Favard's Theorem of Piecewise Continuous Almost Periodic Functions and Its Application[J].J Math Anal Appl,2014,413(1):35-46
[11]张克玉.渐近概周期地Logistic方程[D].哈尔滨:哈尔滨工业大学,2007Zhang Keyu.Asymptotically Almost Periodic Logistic Equation[D].Harbin,Harbin Institute of Technology,2007
[12]Zhang C.Almost Periodic Type Function and Ergodicity[M].Beijing,Science Press,2003
[13]Gaines R E,Mawhin J L.Coincidence Degree and Nonlinear Differential Equation[M].Berlin,Springer-Verlay,1977
[2]Bainov D D,Simeonov P S.Impulsive Differential Equations:Periodic Solutionand Applica-Tions[M].Longman,London,UK,1993
[3]罗振国.具有脉冲干扰的生态数学模型周期解的存在性与全局吸引性[D].长沙:中南大学,2010Luo Zhenguo.Existence and Global Attractivity of Positive Periodic Solutions for Ecological Mathematics Models with Impulses[D].Changsha,Central South University,2010(in Chinese)
[4]李建利.脉冲微分方程边值问题和周期解[D].长沙:湖南大学,2006Li Jianli.Boundary Value Problems and Periodic Solutions of Impulsive Differential Equations[D].Changsha,Hunan University,2006(in Chinese)
[5]傅金波,陈兰荪.基于生态环境和反馈控制的多种群竞争系统的正周期解[J].数学物理学报,2017,37(3):553-561Fu Jinbo,Chen Lansun.Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls[J].Acta Mathematica Scientia,2017,37(3):553-561(in Chinese)
[6]黄勇,黄燕革.具有强迫项的有限时滞Lienard方程周期解的存在性[J].四川师范大学学报:自然科学版,2016,39(1):111-116Huang Yong,Huang Yange.The Existence of Periodic Solutions for a Class of Forced and Finite Delayed Lienard Equations[J].Journal of Sichuan Normal University:Natural Science,2016,39(1):111-116(in Chinese)
[7]汪小明.一类具多个偏差变元Rayleigh型p-Laplacian方程周期解[J].数学研究,2012,5(2):115-123Wang Xiaoming.Periodic Solutions to a Kind of Rayleigh Type P-Laplacian Equation with Deviating Arguments[J].Journal of Mathematical Study,2012,5(2):115-123(in Chinese)
[8]Xie Y,Li X.Almost Periodic Solutions of Single Population Model with Hereditary Effects[J].Appl Math Comput,2008,203(2):690-697
[9]Alzabut J O,Stamov G T,Sermutlu E.Positive Almost Periodic Solutions for a Delay Logarith-Mic Population Model[J].Mathematical and Computer Modelling,2011,53(1):161-167
[10]Wang L,Yu M.Favard's Theorem of Piecewise Continuous Almost Periodic Functions and Its Application[J].J Math Anal Appl,2014,413(1):35-46
[11]张克玉.渐近概周期地Logistic方程[D].哈尔滨:哈尔滨工业大学,2007Zhang Keyu.Asymptotically Almost Periodic Logistic Equation[D].Harbin,Harbin Institute of Technology,2007
[12]Zhang C.Almost Periodic Type Function and Ergodicity[M].Beijing,Science Press,2003
[13]Gaines R E,Mawhin J L.Coincidence Degree and Nonlinear Differential Equation[M].Berlin,Springer-Verlay,1977