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Anti-periodic solutions of nonlinear first order impulsive functional differential equations

✍ Scribed by Yuji Liu

Book ID
115064079
Publisher
SP Versita
Year
2012
Tongue
English
Weight
255 KB
Volume
62
Category
Article
ISSN
0139-9918

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✦ Synopsis

Abstract

The existence of anti-periodic solutions of the following nonlinear impulsive functional differential equations $$
x'(t) + a(t)x(t) = f(t,x(t),x(\alpha _1 (t)), \ldots ,x(\alpha _n (t))),t \in \mathbb{R},\Delta x(t_k ) = I_k (x(t_k )),k \in \mathbb{Z}
$$ is studied. Sufficient conditions for the existence of at least one anti-periodic solution of the mentioned equation are established. Several new existence results are obtained.

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We study the existence of T -periodic solutions of some first order functional differential equations. Several existence criteria are established for our problems; in particular, we obtain conditions for the existence of multiple (even infinitely many) T -periodic solutions of one of the problems. E