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Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays

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Acta Mathematicae Applicatae Sinica 2007年第1期23卷 39-48页

作者： Yan Lv Wei Lv Jian-hua Sun Department of Mathematics Nanjing University Nanjing 210008 China Department of Mathematics Xi'an Jiao Tong University Xi'an 710049 China

By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete... 详细信息

关键词： Predator-prey system time delay positive periodic solution Fredholm operator coincidence degree

PERIODIC SOLUTION AND PERSISTENCE FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY MODEL WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS

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Journal of Systems Science & Complexity 2008年第2期21卷 226-238页

作者： Desheng TIAN College of Sciences Hubei University of Technology Wuhan 430068 China

The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.

关键词： coincidence degree periodic solution predator-prey model ratio-dependent uniform persistence.

Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model

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Chinese Physics B 2012年第1期21卷 24-28页

作者： Wang Na Department of Mathematics East China Normal UniversityShanghai 200241China

We study a time delay equation for the lossless transmission line model. Under suitable conditions, by using the continuation theorem of the coincidence degree theory, the existence of the periodic solution for the no... 详细信息

关键词： periodic solution time delay nonlinearity coincidence degree

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

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Applied Mathematics and Mechanics(English Edition) 2002年第12期23卷 1367-1373页

作者：向兰周进刘曾荣孙姝 Department of Physics Hebei University of Technology Department of Mathematics Shanghai University Shanghai 200436 P R China Department of Mathematics Shanghai University Naval Submarine Academy

Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

关键词： Hopfield neural network periodic solution global exponential stability coincidence degree Liapunov's function

Positive periodic solution for a nonautonomous periodic model of population with time delays and impulses

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 18-24页

作者： ZHOU Gang SHI Bao GAI Ming-jiu ZHANG De-cun Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai264001, China Institute of Systems Science and Mathematics Naval Aeronautical and Astronautical University Yantai China

In this paper, a nonautonomous periodic model of population with time delays and impulses, which arises in order to describe the control of a single population of cells, is studied. By the coincidence degree theory we... 详细信息

关键词： Positive periodic solution impulse coincidence degree time delay.

Periodic Solutions of a Class of Second Order Functional Differential Equations

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Acta Mathematica Sinica,English Series 2005年第1期21卷 95-108页

作者： ZhengQiuZHANG ZhiChengWANG DepartmentofAppliedMathematics HunanUniversityChangsha410082P.R.China

We obtain sufficient conditions for the existence of periodic solutions ofthe following second order nonlinear differential equation: ax(t) + bx^(2k-1)(t) + cx^(2k-1)9t) +g(x(t - τ_1), x(t - τ_2)) = p(t) = p(t + 2π). Our approach is based on the continuation theoremof the coincidence degree, and the priori estimate of periodic solutions.

关键词： Functional differential equation Continuation theorem coincidence degree Periodic solution

SOLVABILITY OF M-POINT BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 1998年第2期18卷 221-226页

作者：张福保 Dept. of Math. Xuzhou Normal Univ Xuzhou 221009 China

In this paper, mainly by means of the coincidence degree method, the existence of solutions for m-point boundary value problems at resonance of second order ordinary differential equations is discussed.

关键词： coincidence degree m-point BVP resonance Caratheodory's conditions

PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS OF MIXED TYPE

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Applied Mathematics and Mechanics(English Edition) 2000年第3期21卷 363-370页

作者：张福保 Department of Mathematics Xuzhou Normal University Xuzhou P R China

The existence of at feast one solution and the existence of extreme solutions of periodic boundary value problems for first-order integro-differential equations of mixed type are studied, in the presence of generalized upper and laver solutions. The discussion is based an new comparison theorems and coincidence degree and monotone iterative methods.

关键词： generalized upper and lower solutions coincidence degree monotone iteration integro-differential equation of mixed type

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1319-1336页

作者： Feng De CHEN Xiao Xin CHEN Jin De CAO An Ping CHEN College of Mathematics and Computer Science Fuzhou University Fuzhou 350002 P. R. China Department of Mathematics Southeast University Nanjing 210096 P R. China Department of Mathematics Xiangnan College Chenzhou 423000 P. R. China

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.

关键词： Positive periodic solutions Delays coincidence degree Single species model