Stability of highly nonlinear hybrid stochastic integro-differential delay equations

Boundedness and Exponential Stability of Highly Nonlinear Stochastic Differential Equations

In this article we consider nonlinear stochastic differential systems and use Lyapunov functions to study the boundedness and exponential asymptotic stability of solutions. We provide several examples in which we consider stochastic systems with unbounded terms.

Nonlinear Integro - Differential Equations

Stability properties of second order delay integro-differential equations

A basic theorem on the behavior of solutions of scalar linear second order delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.

On the Stability of Delay Integro-differential Equations

Some new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.

Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients

This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations(PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Ba...