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Existence and Stability of Almost Periodic Solutions for Quasilinear Delay Systems and the Halanay Inequality

✍ Scribed by Eduardo Liz; Sergei Trofimchuk

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
143 KB
Volume
248
Category
Article
ISSN
0022-247X

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✦ Synopsis

We present some easily verifiable conditions for the existence and global asymptotical stability of almost periodic solutions to systems of delay differential Ž . Ž . Ž . Ž .

Ž n . equations in the form uЈ t s yAu t q Wg t, u q f t , where A, W g L L ‫ޒ‬ t Ž . Ž . and f t , g t, are almost periodic in t uniformly on from bounded subsets of Žw x n . C yh, 0 , ‫ޒ‬ . With this purpose, we use the exponential dichotomy theory together with usual positivity arguments. In particular, the semigroup version of the so-called Perron᎐Frobenius theorem is applied to study the generalized Halanay inequality. Finally, systems with maxima are studied in detail.

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