On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales (original) (raw)

Hyers-Ulam-Rassias stability of abstract second-order linear dynamic equations on time scales

Journal of Mathematics and Computer Science, 2021

In this paper, we obtain new sufficient conditions for Hyers-Ulam and Hyers-Ulam-Rassias stability of abstract second-order linear dynamic equations on time scales. Also a new sufficient condition for the existence and uniqueness of solutions is established, via Banach's fixed point theorem. Finally, two illustrative examples are given to demonstrate the applicability of the theoretical results.

Hyers-Ulam stability of abstract second order linear dynamic equations on time scales

International Journal of Mathematical Analysis, 2014

In this paper we investigate the Hyers-Ulam Stability of the abstract dynamic equation of the form ∆∆ () + () ∆ () + () () = (), ∈ , where , : → L(), the space of all bounded linear operators from a Banach space into itself, and is rd-continuous from a time scale to. Some examples illustrate the applicability of the main result.

Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

We establish the Hyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.

Elements of Lyapunov stability theory for dynamic equations on time scale

International Applied Mechanics, 2007

Stability of dynamic equations on time scale is analyzed. The main results are new conditions of stability, uniform stability, and uniform asymptotic stability for quasilinear and nonlinear systems Keywords: dynamic equations on time scales, stability, uniform stability, asymptotic stability, nonlinear integral inequality, Lyapunov functions On the occasion of the 150th birthday of A. M. Lyapunov