EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR VOLTERRA INTERGO-DIFFERENTIAL EQUATIONS

This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.

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

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 obtain the conditions for the existence of periodic solution of this system.

Existence of Three Positive Periodic Solutions of Neutral Nonlinear Functional Difference Equations

This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.

Multiple Positive Periodic Solutions for Functional Differential Equations with Infinite Delay

In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.

POSITIVE PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

The nonlinear differential equationx′(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 least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.

Existence of Positive Periodic Solutions for Two Species Population Growth Model

Existence and nonexistence criteria are established for the positive periodic solutions of two species population growth with periodic delay by applying continuation theorem of coincidence degree theory.

Positive Periodic Solutions for Three Species Lotka-Volterra Mixed Ecosystems with Periodic Stocking

By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.

Existence of Positive Periodic Solutions for the Predator-Prey Difference System with Beddington-DeAngelis Functional Response and Time Delays

A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response, diffusion, and time delays is investigated. The model consists of n competing preys and one predator, and the predator and one prey are confined to one patch. First, eon^pts and results concerning the continuation theorem of coincidence degree are summarized. Then, a system of algebraic equations is proved to have a unique solution. Finally, the sufficient conditions for the existence of a difference system are established. The result is substantiated through numerical simulation.

The Existence of Positive Periodic Solutions for a Kind of Delay Logistic Equations

In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple positive periodic solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.

Positive Periodic Solutions of Nonautonomous Delayed Predator-Prey System with Pulse Controls

In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other predators consume prey according to the Beddington-DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions of nonautonomous predator-prey system with impulses and periodic delays is obtained under suitable conditions.

ON THE PERSISTENCE AND POSITIVE PERIODIC SOLUTION FOR PLANAR COMPETING LOTKA-VOLTERRA SYSTEMS

We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.

On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments

By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation

Positive Periodic Solution for a Nonautonomous Delay Differential Equation

Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.

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

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.

EXISTENCE AND GLOBAL ATTRACTIVITY OF POSITIVE PERIODIC SOLUTION OF A LOGISTIC GROWTH SYSTEM WITH FEEDBACK CONTROL AND DEVIATING ARGUMENTS

In this paper, we study the existence and global attractivity of positive peri- odic solutions of a Logistic growth system with feedback control and deviating arguments. A sufficient condition is derived for the existence of a unique peri- odic solution with strictly positive components which is globally asymptotically stable by using the method of coincidence degree and Liapunov functional. Some new results are obtained. The known results are improved and generalized.

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

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 and continuously distributed delays.

Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model

By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r 1 and r 2 are continuous ω-periodic functions in R + = [0,∞) with are positive continuous ω-periodic functions in R + = [0,∞), b i (i = 1, 2) is nonnegative continuous ω-periodic function in R + = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.

POSITIVE PERIODIC SOLUTION OF A NEUTRAL PREDATOR-PREY SYSTEM

In this paper, the existence o f a positive periodic solution to the following neutral predator_prey system (t)=rH(t)1-a 1(t)H(t-τ)+a 2(t-τ)K-α(t)H(t)P(t), (t)=-b(t)P(t)+β(t)H(t)P(t) is studied,in which r,a 2,K and τ are positive constants, and a 1(t ),α(t),b(t) and β(t) are positive continuous functions of period ω .

EXISTENCE AND GLOBAL STABILITY OFPOSITIVE PERIODIC SOLUTION IN A LOGISTIC INTEGRODIFFERENTIAL EQUATION WITH FEEDBACK CONTROL

Sufficient conditions are obtained for the existence and global stability of a positive periodic solution in a periodic logistic integrodifferential equation with feedback control by using the technique of coincidence degree and Lyapunov functional.