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.

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.

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 OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.

TWIN POSITIVE PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, the author studies a class of nonlinear functional differential equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of twin positive periodic solutions.

MULTIPLE POSITIVE PERIODIC SOLUTIONS TO SINGULAR DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY

By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenvalue of the relevant linear operator. The results in this paper are optimal and totally generalize many present results.

POSITIVE PERIODIC SOLUTIONS OF THE FIRST-ORDER SINGULAR DISCRETE SYSTEMS

In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.

EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION

In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.

TWO POSITIVE PERIODIC SOLUTIONS OF NONLINEAR INTEGRAL EQUATION ON THE INFINITE INTERVAL MODELLING INFECTIOUS DISEASE

In this paper, by applying Avery-Henderson fixed point theorem in a cone, we establish some new existence results of two positive periodic solutions for a type of nonlinear integral equations with variant delay.

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

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.