The Existence of Periodic Solutions of a Class of <i>n</i>-Degree Polynomial Differential Equations*

This paper deals with a class of n-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (n is an odd number) or two (n is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term.

Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations

The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.

Existence and uniqueness of periodic solutions for forced Liénard-type equations

By using topological degree theory and some analysis skill, some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced Lienard-type equations are obtained.

Nonrecurrence Theorems of Periodic Solutions for Functional Differential Equations

nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.

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.

PERIODIC SOLUTIONS OF THIRD-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS

The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.

Periodic Solutions for a Class of Forced Lienard-type Equations

By applying the topological degree theory, we establish some sufficientconditions for the existence on T-periodic solutions for the Liénard-type equation x' + Σ from i=1to n of h_i(x)|x'|^(2α_i) + f_1(x)|x'|~2 + f_2(x)x' + g(t,x) = p(t). Our results extend andimprove some known results in the literature.

PERIODIC SOLUTIONS FOR NEUTRAL LINARD EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

Using the theroy of topological degree, the paper studies the periodic solutions to a type of neutral Liénard equation with state-dependent deviation variable. A sufficient condition for the existence of periodic solution is obtained.

Existence of Periodic Solutions for Neutral Functional Differential Equations with Nonlinear Difference Operator

In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.

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 and Uniqueness of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equations with Constant Delays

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form （x（t）＋Bx（t-δ））＂＋Cx＇（t）＋g（x（t-τ））=p（t）.

Periodic Solutions of a Class of Second Order Functional Differential Equations

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.

PERIODIC SOLUTION TO A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

We obtain sufficient conditions for class of second order neutral functional theorem of the coincidence degree. the existence of periodic solution to a differential equation, using continuation

PERIODIC SOLUTIONS FOR HIGHER ORDER DELAY FUNCTIONAL DIFFERENTIAL EQUATION OF NEUTRAL TYPE WITH LINEAR RESTORING TERMS

Using the theory of coincidence degree, the authors studied the existence of periodic solutions for higher order delay functional differential equations of neutral type with restoring terms and some new results for the existence of periodic solutions have been obtained.

EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH TWO DEVIATING ARGUMENTS

In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.

2π-PERIODIC SOLUTION OF THE EQUATION x + f(x)x + bx + g(x(t - т)) = p(t)

In this paper, time delay Lienard's equations are considered, by using the theory of concidence degree, a sufficient condition of existence of at least one 2π-periodic solution is obtained.

PERIODIC SOLUTIONS FOR A LINARD-TYPE EQUATION WITH DELAYS

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard-type equation with delays.