Inequalities and sufficient conditions for exponential stability and instability for nonlinear Volterra difference equations with variable delay

Ernest Yankson

doi:10.4067/S0719-06462021000100109

DOI:

https://doi.org/10.4067/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.

Keywords

Exponential stability , Lyapunov functional , Instability

Ernest Yankson Department of Mathematics, University of Cape Coast, Ghana.

Pages: 109–119
Date Published: 2021-04-14
Vol. 23 No. 1 (2021)

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