Existence and Uniqueness of Positive Periodic Solutions for First-order Functional Differential Equations

In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.

Existence and Uniqueness of Almost Periodic Solutions for Some Infinite Delay Integral Equations

In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.

ON THE EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTIONS TO DISCRETE TWO-SPECIES COMPETITIVE SYSTEMS

In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are obtained.

THE EXISTENCE AND UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES

This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.

ON THE EXISTENCE AND UNIQUENESS OF SOLUTION OF IMPLICIT HYBRID METHODS

In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.

THE EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTION OF x"+cx'+g(x)=P(t,x)

This paper studies equation x' + cx' + g(x) = P(t,x). Under some suitable conditions the existence and uniqueness of almost periodic solution of this equation are given.

Existence and Uniqueness of Anti-periodic Solutions for 2n-order Differential Equations

In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.

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.

Periodic Solutions of Singular Neutral Differential Systems with Infinite Delay

In this paper,we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay.By using matrix measure and Krasnoselskii＇s fixed point theorem,we obtained the suffcient conditions of the existence of periodic solutions.

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.

Existence and Uniqueness of Solutions to Random Impulsive Differential Systems

The existence and uniqueness in mean square of solutions to certain random impulsive differential systems is discussed in this paper. Cauchy-Schwarz inequality, Lipschtiz condition and techniques in stochastic analysis are employed in achieve the desired results.

On the Existence,Uniqueness and Stability of Periodic Solutions of Large Scale Systems with Unbounded Delay

In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.

Existence of Periodic Solutions for Differential Inclusions

This paper deals with the periodic solution theory to differential inclusions related to periodic optimal control problems. The results of Halanay and Yoshizawa are presented for multivalued systems.

Periodic Solutions of Some Polynomial Differential Systems in R<sup>4</4>

We provide sufficient conditions for the existence of periodic solutions of the polynomial fourth order differential system , where A is a 4 × 4 constant matrix, P1, P2, P3 and P4 are polynomials in the variables x, y, u, v of degrees n, hi(t) = hi(t + 2π) with i = 1, 2, 3, 4 being periodic functions and ε is a small parameter.

Construction of Periodic Solutions of One Class Nonautonomous Systems of Differential Equations

In this article we proposed a method for constructing approximations to periodic solutions of one class nonautonomous system of ordinary differential equations. It is based on successive approximation scheme using parallel symbolic calculations to obtain solutions in analytical form. We showed the convergence of the scheme of successive approximations on the period, and also considered an example of a second order system where the described scheme of calculations can be applied.

Existence and Uniqueness of Global Solution for Certain Degenerate Reaction-Diffusion Systems

In this paper we discuss the following nonlinear degenerate parabolic systems u_i=△a_i(u_i)+b_i(x,t,u_i)Du_i+f_i(x,t,u)for i = 1,2, …, m and u = (u_1,…, u_m) is a vector function, with Dirichlet boundary condition. Under some structure conditions on a_i,b_i and f_i and initial data u_i^o∈Li(Ω) for some pi>p_i^o = 1,2,…,m, the result on existence and uniquence of global solution is established.

NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTION TO A CLASS OF HIGHER DIMENSIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,using fixed point method,we discuss the problem of periodic solution to a class of higher dimensional functional differential equation.Our results extend and improve some results of the previous researches.

UNIQUE EXISTENCE OF PERIODIC SOLUTIONS OF NEUTRAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS

This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.