A SIMPLIFIED PROOF TO A THEOREM BY DING TONG-REN ON PERIODIC SOLUTIONS OF DUFFING EQUATIONS

In 1982, DING Tong-ren gave a basic theorem about existence of periodic solutions of Duffing equations with double resonance. A simplified proof will be given by making use of the Leray-Schauder principle.

Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method

This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation x^（2n） ＋ g（x） = e（t） （n ≥ 1）. Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically.

2π-periodic Solution for a Kind High Order Delay Duffing Equation

In this paper, the high order delay Duffing equation ax^（2n） ＋bx＋g（x（t-r）） = p（t） are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained.

Positive Periodic Solutions for Nonautonomous Differential Equations with Delay

By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.

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.

A PRIORI BOUNDS FOR PERIODIC SOLUTIONS OF A KIND OF THIRD-ORDER DELAY DIFFERENTIAL EQUATION

By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solutions of a kind of third-order neutral delay functional differential equation with deviating arguments.

A Study of Periodic Solution of a Duffing’s Equation Using Implicit Function Theorem

In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.

Stability Analysis of Periodic Solutions of Some Duffing’s Equations

In this paper, some stability results were reviewed. A suitable and complete Lyapunov function for the hard spring model was constructed using the Cartwright method. This approach was compared with the existing results which confirmed a superior global stability result. Our contribution relies on its application to high damping door constructions. (2010 Mathematics Subject Classification: 34B15, 34C15, 34C25, 34K13.)

Almost Periodic Solutions for Nonlinear Duffing Equations

The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an intersting result on the existence of almost periodic solutions.

Existence of Periodic Solutions of Nonlinear Neutral Differential Equation with Deviating Argument

Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.

Constructive proof on the existence of periodic solution of Duffing equation

CONSIDER the following boundary value problem of Duffing equation:{x(t)+Cx’(t)+g(t,x)=e(t), x(0)-x’(zπ)=x’(0)-x’(2π)=0,} (1)where g: R×R→R is continuous and continuously differentiable with respect to x, continu-ous and 2π-periodic with respect to t. C is a constant. e: R→R is continuous and 2π-period-ic. If there exist two almost everywhere continuous functions a(t), b(t)

ALMOST PERIODIC SOLUTIONS OF NONLINEAR DUFFING'S EQUATIONS WITH DELAY

We consider the delay Duffing equation wilers g uniformly almost periodic in t. We provide existence, uniqueness results for almost periodic soltltion of eq.(1), the method of approach uses sub and supersolutions and degree theory.

The Existence of 2π-periodic Solutions for Duffing Equation x+g(x(t-τ))=p(t) With Delay

Many papers have been published on the existence of periodic solutions for the Duffing equation (?)+g(x)=p(t)=p(t+2π).(1) Their main assumptions imposed on g are super-linear, sub-linear and exclude the resonance cases (see Ref. [1] and Prof. T. R. Ding’s, Prof. W.G. Ge’s recent papers). Relatively speaking, there are few papers concerning the

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.

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.

ON ALMOST PERIODIC SOLUTIONS TO THIRD-ORDER NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.

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.

Existence and Uniqueness of 2π-Periodic Solution About Duffing Equation and Its Numerical Method

A new provement of the existence and uniqueness about periodic boundary value Duffing equation is established by using global inverse function theorem. An algorithm for solving differential equation that has a large convergence domain is given. Finally, a numerical example is given.

ON PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R^n,which is an extension of Mawhin's existence theorem of periodic solutions of F.D.Es with finite delay.Second,as an application of it,we obtain the existence theorem of positive periodic solutions of the Lotka-Volterra equations:dx(t)/dt=x(t)(a-kx(t)-by(t)),dy(t)/dt=-cy(t)+d integral from n=0 to +∞ x(t-s)y(t-s)dμ(s)+p(t).