Ulam stability and instability of first-order linear $\omega$-periodic dynamic equations on isolated time scales

D. R. Anderson and M. Onitsuka

We apply a new definition of periodicity on isolated time scales introduced
by Bohner, Mesquita, and Streipert to the study of Ulam stability. If the
graininess (step size) of an isolated time scale is bounded by a finite constant,
then the linear ω.-periodic dynamic equations are Ulam stable if and only if the
exponential function has modulus different from unity. If the graininess increases
at least linearly to infinity, the ω.-periodic dynamic equations are not Ulam stable.
Several examples of specific isolated time scales are also supplied.

Springer volume Functional Differential Equations and Dynamic Equations on time scales - With Applications to Continuum Mechanics

Birkhauser

17

39

https://doi.org/10.1007/978-3-031-83327-4