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Asymptotic stability of nonlinear functional differential equations

Sengadir, T (1997) Asymptotic stability of nonlinear functional differential equations. In: Nonlinear Analysis Theory, Methods & Applications,, 28 (12). pp. 1997-2003.

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In this paper, we study asymptotic stability of solutions of the following functional differential equation: x'(t) = a(t)x(t) + b(t)x(p(t)) + f ( t , x(t), x(p(t))) x(O) = xo. (1) Here a,b : [0, oo) ~ C, f : [0, oo) × C × C ~ C are continuous functions, x0 E C and p : [0, oo) ~ [0, oo) is a continuously differentiable function such that the following conditions hold: (i) limt_oo p(t) = oo (ii) p(t) < t, t E [0, co) (iii) 0 * limt_oo p' (t) < oo. The technical condition (iii) holds, for example, for the case of proportional delays. Our results can be generalised for equations with finite number of delays and also for systems. To achieve the latter, use of logarithmic norm (cf. [1]) of a matrix is essential. For the ease of presentation, however, we consider only the simplest case. Earlier, asymptotic stability of solutions of the neutral functional differential equation.

Item Type: Journal Article
Publication: Nonlinear Analysis Theory, Methods & Applications,
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Functional differential equations;asymptotic stability.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Mar 2009 05:48
Last Modified: 19 Sep 2010 05:01
URI: http://eprints.iisc.ac.in/id/eprint/18430

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