𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Stability and periodicity in dynamic delay equations

✍ Scribed by Murat Adıvar; Youssef N. Raffoul

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
492 KB
Volume
58
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

Let T be an arbitrary time scale that is unbounded above. By means of a variation of Lyapunov's method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations

Moreover, if T is a periodic time scale, then necessary conditions are given for the existence of a unique periodic solution of the above mentioned equation.

📜 SIMILAR VOLUMES

Stability in linear delay equations
Stability in linear delay equations
✍ Jack K Hale; Ettore F Infante; Fu-Shiang Peter Tsen 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 879 KB
Stability for first order delay dynamic
Stability for first order delay dynamic equations on time scales
✍ Haihua Wu; Zhan Zhou 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 264 KB

In this paper, we establish some sufficient conditions for the uniform stability and the uniformly asymptotical stability of the first order delay dynamic equation where T is a time scale, p(.) is rd-continuous and positive, the delay function τ : T → (0, r ]. Our results unify the corresponding on

Oscillation and stability in nonlinear d
Oscillation and stability in nonlinear delay differential equations of population dynamics
✍ I. Kubiaczyk; S.H. Saker 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 453 KB

this paper, we shall study the oscillation of all positive solutions of the nonlinear delav differential eouation and x'(t) + ckvmx(t)xn(t -7) x @+x"(t-7) = ' x'(t) + p(t) -F(t) r+xn(t-T) = 0 (\*\*) about their equilibrium points. Also, we study the stability of these equilibrium points and prove