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Stability of nonlinear Volterra equations

Ngoc P. H. A., Hieu L. T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 3

333--340

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

Fractional white noise perturbations of parabolic Volterra equations

Sperlich S., Wilke M.

Journal of Applied Analysis

2010

Vol. 16, nr 1

31-48

Aim of this work is to extend the results of Clément, Da Prato and Prüss [5] on the fractional white noise perturbation with Hurst parameter H ∈ (0,1). We will obtain similar results and it will turn out that the regularity of the solution u(t) increases with Hurst parameter H.