Theoretical analysis demonstrates stability and boundedness criteria for first-order linear delay dynamic equations on time scales, highlighting the utility of a local jump condition.
In this paper, we analyze the boundedness of solutions to nonhomogeneous first‐order linear delay dynamic equations on time scales containing a term with the forward shifted delay function, and we examine the stability of the corresponding homogeneous equation. Three kinds of stabilities are investigated with the application of an appropriate Lyapunov‐Krasovskii functional. In addition, a local jump condition is introduced to facilitate the results. Suitable examples are provided to check the applicability of the results.
No takes yet. Share an insight, caveat, or question.
D’Costa et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: