Inequalities and sufficient conditions for exponential stability and instability for nonlinear Volterra difference equations with variable delay
Author
Yankson, Ernest
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/260310.4067/S0719-06462021000100109
Abstract
Inequalities and sufficient conditions that lead to exponential stability of the zero solution of the variable delay nonlinear Volterra difference equation\(\begin{eqnarray*}x(n+1)=a(n)h(x(n))+\sum^{n-1}_{s=n-g(n)}b(n,s)h(x(s))\end{eqnarray*}\)
are obtained. Lyapunov functionals are constructed and employed in obtaining the main results. A criterion for the instability of the zero solution is also provided. The results generalizes some results in the literature.