Inequalities and sufficient conditions for exponential stability and instability for nonlinear Volterra difference equations with variable delay
- Ernest Yankson ernestoyank@gmail.com
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DOI:
https://doi.org/10.4067/S0719-06462021000100109Abstract
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.
Keywords
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