具偏差变元的高阶中立型泛函微分方程的周期解存在性问题

利用 Fourier 级数理论,伯努利数理论和重合度理论研究了一类具偏差变元的高阶中立型泛函微分方程的周期解问题,得到了周期解存在的充分条件.     

On the existence of periodic solutions for a kind of high-order neutral functional differential equation

By using the coincidence degree theory of Mawhin, we study a kind of high-order neutral functional differential equation with distributed delay as follows:

     

Periodic solutions for a kind of second order neutral functional differential equations

In this paper, criteria are established for the existence of periodic solutions to a second order sublinear neutral differential equation. Our method is based on careful a priori estimation and continuation theorem, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Periodic solutions of the third order functional differential equations

We obtain sufficient conditions for the existence of periodic solutions of the following third order nonlinear functional differential equations

     

一类非线性中立型微分方程周期解的存在性

利用有关不等式,本文首先获得一类非线性中立型微分方程一个新的先验估计.基于解的先验估计以及迭合度理论,给出了这类中立型微分方程存在周期解的一个充分条件.     

Periodic solutions for higher order differential equations with deviating argument

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for higher order differential equations with deviating argument . Some new results on the existence of periodic solutions of the equations are obtained. Meanwhile, an example is given to illustrate our results.     

Three periodic solutions for a nonlinear first order functional differential equation

This paper is concerned with the existence of three positive T-periodic solutions of the first order functional differential equations of the form

x^′(t)=a(t)x(t)-λb(t)f(t,x(h(t))),     

Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay

This paper investigates the existence and uniqueness theorem of solutions to neutral stochastic differential equations with infinite delay (short for INSFDEs) at a space BC((-∞,0];R^d). Under the uniform Lipschitz condition, linear growth condition is weaken to obtain the moment estimate of the solution for INSFDEs. Furthermore, the existence, uniqueness theorem of the solution for INSFDEs is derived, and the estimate for the error between approximate solution and exact solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence, uniqueness theorem is also valid for INSFDEs on [t₀,T]. Moreover, the existence, uniqueness theorem still holds on interval [t₀,∞), where t₀∈R is an arbitrary real number.     

Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations

Consider the forced higher-order nonlinear neutral functional differential equation

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.     

Existence of positive periodic solutions of first order neutral differential equations with variable coefficients

This work deals with the existence of positive $\omega$-periodic solutions for the first order neutral differential equation. The results are established using Krasnoselskii’s fixed point theorem. An example is given to support the theory.     

Existence of solutions for impulsive partial neutral functional differential equations

This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations.     

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

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of forced Rayleigh equation of the form

x^″+f(x^′(t))+g(t,x(t))=e(t).     

Existence of periodic and subharmonic solutions for second order functional difference equations

In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.     

Existence and uniqueness of periodic solutions for a class of nonlinear n ‐th order differential equations with delays

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T ‐periodic solutions for a class of nonlinear n ‐th order differential equations with delays of the form x⁽ⁿ⁾(t) + f (x^{(n‐ 1)}(t)) + g (t, x (t ‐ τ (t))) = p (t).     

Existence for nonoscillatory solutions of second-order nonlinear differential equations

In this paper, the existence of nonoscillatory solutions of the second-order nonlinear neutral differential equation

     

Existence theory for first order discontinuous functional differential equations

We prove the existence of extremal solutions for a first order functional differential equation subject to nonlinear boundary conditions of functional type. Moreover, the functions that define our problem are allowed to be discontinuous. The proof of our main result is based on a generalized iterative technique.