Periodicity and stability in neutral nonlinear differential equations with functional delay
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Date
2005-12-06
Authors
Dib, Youssef M.
Maroun, Mariette R.
Raffoul, Youssef N.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We study the existence and uniqueness of periodic solutions and the stability of the zero solution of the nonlinear neutral differential equation
d/dt x(t) = -α(t)x(t) + d/dt Q(t, x(t - g(t))) + G(t, x(t), x(t - g(t))).
In the process we use integrating factors and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution and the asymptotic stability of the zero solution provided that Q(0, 0) = G(t, 0, 0) = 0.
Description
Keywords
Krasnoselskii, Contraction, Neutral differential equation, Integral equation, Periodic solution, Asymptotic stability
Citation
Dib, Y. M., Maroun, M. R., & Raffoul, Y. N. (2005). Periodicity and stability in neutral nonlinear differential equations with functional delay. <i>Electronic Journal of Differential Equations, 2005</i>(142), pp. 1-11.