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))].

Periodic boundary value problem for the first order functional differential equations with impulses

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.

Periodic Boundary Value Problem for Functional Differential Equations with Impulses

Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.

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.

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.

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.

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.

Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions

Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to the PDDE as a linear operator over the space of initial conditions. This approximation allows us to consider the state space as finite dimensional resulting in a finite matrix approximation whose spectrum converges to the spectrum of the monodromy operator.

Pseudo Almost Periodic Solutions for Second Order Abstract Differential Equations

On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract differential equation ( u″(t)+A 1u′(t)+A 0u(t)=0, t≥0 ) is strongly well posed, the necessary conditions for their solutions to be pseudo almost periodic are derived.

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.

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.

A Note on a Functional Differential Equation with State Dependent Argument

This paper is concerned with solutions of a functional differential equation. Using Krasnoselskii’s fixed point theorem, the solutions can be obtained from periodic solutions of a companion equation.

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.

Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.

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.

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 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.