15,792 research outputs found
A note on “Stability and periodicity in dynamic delay equations” [Comput. Math. Appl. 58 (2009) 264–273]
AbstractThe purpose of this note is twofold: First we highlight the importance of an implicit assumption in [Murat Adıvar, Youssef N. Raffoul, Stability and periodicity in dynamic delay equations, Computers and Mathematics with Applications 58 (2009) 264–272]. Second we emphasize one consequence of the bijectivity assumption which enables ruling out the commutativity condition δ∘σ=σ∘δ on the delay function
Halanay type inequalities on time scales with applications
This paper aims to introduce Halanay type inequalities on time scales. By
means of these inequalities we derive new global stability conditions for
nonlinear dynamic equations on time scales. Giving several examples we show
that beside generalization and extension to q-difference case, our results also
provide improvements for the existing theory regarding differential and
difference inequalites, which are the most important particular cases of
dynamic inequalities on time scales
- …