Existence Results For Nonlinear Abstract Neutral Differential Equations With Time Varying Delays∗

Differential transformation method for solving a neutral functional-differential equation with proportional delays

In this article differential transformation method (DTMs) has been used to solve neutral functional-differential equations with proportional delays. The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. Exact solutions can also be obtained from the kno...

Invariant and attracting sets of non-autonomous impulsive neutral integro-differential equations

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Homoclinic Solutions for a Class of Nonlinear Second-order Differential Equations with Time-varying Delays

In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we obtain some sufficient conditions for the existence of homoclinic solutions for a class of nonlinear second-order differential equations with timevarying delays. Moreover, we give an example to illustrate the feasibility of obtained results. Our results are completely new.