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

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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.

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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.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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