Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale
Date
2007-02-12
Authors
Kaufmann, Eric R.
Raffoul, Youssef N.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel'skiĭ to show that the nonlinear neutral dynamic equation with delay
xΔ(t) = -α(t)xσ (t) + (Q(t, x(t), x(t - g(t)))))Δ + G(t, x(t), x(t - g(t))), t ∈ T,
has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid of the contraction mapping principle we study the asymptotic stability of the zero solution provided that Q(t, 0, 0) = G(t, 0, 0) = 0.
Description
Keywords
Krasnosel'skii, Contraction mapping, Neutral, Nonlinear, Delay, Time scales, Periodic solution, Unique solution, Stability
Citation
Kaufmann, E. R., & Raffoul, Y. N. (2007). Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale. <i>Electronic Journal of Differential Equations, 2007</i>(27), pp. 1-12.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.