On the integro-differential inequality ∥f′∥22 ⩽ K ∥f∥p∥f″∥q

L–operator Integro–differential Inequality for Dissipativity of Stochastic Integro–differential Equations

In this paper, Itô stochastic integro-differential equations are considered. By establishing an L -operator integro-differential inequality and using the properties of M -cone and stochastic analysis technique, we obtain some new sufficient conditions ensuring the exponential p -dissipativity of the stochastic integro-differential equations. An example is also discussed to illustrate the effici...

Integro - Differential Stochastic Resonance

A new class of stochastic resonator (SRT) and Stochastic Resonance (SR) phenomena are described. The new SRT consist of a classical SRT, one or more time derivative circuits and the same number of time integrators. The incoming signal with additive noise is first time derivated, then passes through the classical SRT and finally it is time integrated. The resulting SR phenomena show a well defin...

Integro - Partial Differential

We consider an approximation scheme for integro-partial differential equations which arise in the theory of linear viscoelas-ticity. This scheme is based on a modiication (to account for the singular kernel) of certain averaging type approximation methods for delay equations. We use this scheme to investigate the eeects of a history parameter (the delay length) on the behavior of the eigenvalue...

On a class of integro-differential problems

Nonlinear Integro - Differential Equations