Exponential Stability of Volterra Integro Dynamic Equations on Time Scales

2025
Shraddha Ramanbhai Christian, Andrejs Reinfelds

In this paper, we give new sufficient conditions for boundedness and exponential stability of solutions for nonlinear Volterra integro dynamic equations from above on unbounded time scales using first Lyapunovs method. To prove this result we reduce the n-dimensional problem to the corresponding scalar one using the concept of matrix measure and a new simpler proof of Coppel’s inequality on the time scales. There is an example that illustrates the conditions of the theorem

Keywords
Volterra integro dynamic equations, time scales, matrix measure, Coppel's inequality, boundedness, exponential stability.
DOI
10.3390/math13243918
Hyperlink
https://www.mdpi.com/2227-7390/13/24/3918

Christian, S., Reinfelds, A. Exponential Stability of Volterra Integro Dynamic Equations on Time Scales. The Humanities and Social Sciences / Humanitārās un sociālās zinātnes, 2025, Vol. 13, No. 24, Article number 3918. ISSN 2227-7390. Pieejams: doi:10.3390/math13243918

Publication language
English (en)