THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.

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 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 SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.

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

Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

Existence of Periodic Solution for a Kind of Functional Differential Equation

In this paper,a kind of high order functional differential equation is considered.By using the theory of concidence degree,a sufficient condition of existence of at least one 2π-period solution is obtained.

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.

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.

Entire solutions of a certain type of functional-differential equations

In this paper, we shall utilize Nevanlinna value distribution theory and normality theory to study the solvability of a certain type of functional-differential equations. We also consider the solutions of some nonlinear differential equations.

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.

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.

POSITIVE SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper is to obtain sufficient conditions under which the neutral functional differential equation d/dx[x(t) + integral(c)(t) x(s)d(s) mu(t, s)] + integral(c)(t) f(t, x(s))d(s) eta(t, s) = 0, t greater than or equal to t(0) greater than or equal to c (1) has a positive solution on [c, +infinity). Some results in [1] are generalized. Then we apply our results to functional differential equations of special form and obtain sufficient conditions for those equations to have a positive solution.

SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations（a（t）x＇（t））＇＋δ1p（t）x＇（t） ＋δ2q（t）f（x（g（t））） = 0,for 0 ≤ to≤ t, where 51 = ：El and δ±1. The functions p,q,g ： [t0, ∞） → R, f ： R → are continuous, a（t） 〉 0,p（t） ≥0,q（t） 〉 0 for t ≥ to,lirn g（t） = ∞, and q is not identically zero on any subinterval of [to, ∞）. Moreover, the functions q（t）, g（t）, and a（t） are continuously differentiable.

Global Solutions and Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay

This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.

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.

Oscillation Criteria for Even Order Functional Differential Equations with Damped Term

This paper investigates a class of even order functional differential equations with damped term,and derives two new oscillatory criteria of solution.

OSCILLATION FOR SOLUTIONS OF SYSTEMS OF N-TH ORDER PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.

OSCILLATION AND EXISTENCE OF POSITIVE SOLUTIONS FOR NEUTRAL DIFFERENTIAL EQUATIONS

New sufficient conditions for the oscillation of all solutions of the neutral differential equation [x(t) - p(t)x(t -τ)]' + Q(t)x(t -σ) = 0 are obtained, which further answers an open problem proposed by Gyori and Ladas. An necessary and sufficient condition for the existence of positive solutions is also obtained which partially solves an open problem proposed by Chuanxi and Ladsa and which has been be proved in [9], but we give a new proof.

On the Counting Functions of Meromorphic Solutions of Systems of Higher-order Algebraic Differential Equations

Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.