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))].

Periodic Solutions in UMD Spaces for Some Neutral Partial Functional Differential Equations

The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.

PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

The problem of periodic solutions for a kind of kth-order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder's fixed point principle, a kind of kth-order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well. These results improve and extend some known results in recent literature.

STABILITY AND ALMOST PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). For periodic Eq. (1), we prove that if Eq. (1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to H.f(ξ),then Eq. (1 ) has an mω -- periodic solution p(t), for some integer m ≥1. Furthermore, we prove that if almost periodic Eq. (1 ) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq. (1) has an almost periodic solution.

EXISTENCE OF PERIODIC SOLUTIONS TO A p-LAPLACIAN NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH VARIABLE PARAMETER

By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.

THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE 0F PERIODIC SOLUTIONS OF A TYPE OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.

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

A Priori Bounds for Periodic Solutions of a Kind of Second Order Neutral Functional Differential Equation with Multiple Deviating Arguments

Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows：（x（t）-^n∑i=1cix（t-ri））″=f（x（t））x′＋g（x（t-τ））＋p（t）.In order to do so, we analyze the structure of the linear difference operator A ： C2π→C2π, [Ax]（t） =x（t）-∑^ni=1cix（t-ri）to determine some flmdamental properties first, which we are going to use throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating a priori bounds of periodie solutions.

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）.

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.

Periodic Solutions to a Kind of Second Order Neutral Functional Differential Equation in the Critical Case

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows：（x（t） - cx（t -τ）＂ = g（t, x（t - μ（t））） ＋ e（t）,in the critical case ｜c｜ = 1. By employing Mawhin＇s continuation theorem and some analysis techniques, some new results are obtained.

EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF n-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.

PERIODIC SOLUTIONS TO A HIGH-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained.

STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.

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

Existence of p-mean Almost Periodic Mild Solution for Fractional Stochastic Neutral Functional Differential Equation

A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.

EXISTENCE OF PERIODIC SOLUTION FOR A KIND OF THIRD-ORDER GENERALIZED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH VARIABLE PARAMETER

In this paper, we investigate a third-order generalized neutral functional differential equation with variable parameter. Based on Mawhin’s coincidence degree theory and some analysis skills, we obtain sufficient conditions for the existence of periodic solution for the equation. An example is also provided.

POSITIVE PERIODIC SOLUTION TO SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH MIXED DELAY

We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii’s fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.

Periodic solutions of periodically perturbed functional differential equations

By using the generalized degree theory, some periodically perturbed functional differential equations have been proved to have at least one periodic solution if the associated homogeneous linear equations have no nontrivial periodic solution. Some known results are generalized.

Existence of Homoclinic Solutions for a Class of Neutral Functional Differential Equations

By means of Mawhin＇s continuation theorem and some analysis methods, the existence of 2kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above periodic solutions set.