1. PERIODICITY AND STABILITY IN NEUTRAL NONLINEAR DIFFERENTIAL EQUATIONS WITH FUNCTIONAL DELAY.
- Author
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Dib, Youssef M., Maroun, Mariette R., and Raffoul, Youssef N.
- Subjects
- *
DIFFERENTIAL equations , *ASYMPTOTIC theory of algebraic ideals , *MATHEMATICAL mappings , *FIXED point theory , *NONLINEAR operators , *NONLINEAR integral equations - 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) = -a(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. [ABSTRACT FROM AUTHOR]
- Published
- 2005