Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral differential equation are established.

The global stability behavior of a non-autonomous neutral functional integro-differential equation is studied. A sufficient condition for every solution of this equation to tend to zero is given.

Term structure models give the dependence of time to maturity of a discount bond and its present price. One-factor models are often formulated in terms of a stochastic differential equation for the instantaneous interest rate (short rate). In the theory of nonarbitrage term structure models the bond prices (yielding the interest rates) are given by a solution to a parabolic partial differential...

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolatio...

In this paper, we present a numerical integration method to solve singularly perturbed delay differential equations. In this method, we first convert the second order singularly perturbed delay differential equation to first order neutral type delay differential equation and employ the numerical integration. Then, linear interpolation is used to get three term recurrence relation which is solve...

We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems relate...

Recently, we initiated in [Systems Control Lett., 26 (1995), pp. 245–251] the study of exponential stability of neutral stochastic functional differential equations, and in this paper, we shall further our study in this area. We should emphasize that the main technique employed in this paper is the well-known Razumikhin argument and is completely different from those used in our previous paper ...