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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Almost Periodic Solutions
verfasst von : Marat Akhmet
Erschienen in: Nonlinear Hybrid Continuous/Discrete-Time Models
Verlag: Atlantis Press
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This chapter presents existence and stability of almost periodic solutions of the following system
$$ {\frac{dx(t)}{dt}} = A(t)x(t) + f(t,x(\theta_{\upsilon (t) - p1} ),x(\theta_{\upsilon (t) - p2} ), \ldots ,x(\theta_{\upsilon (t) - pm} )), $$
(7.1) where
$$ x \in \mathbb{R}^{n} ,\;t \in \mathbb{R}, $$
υ
(
t
) = 1 if
θ
i
≤
t
<
θ
i
+1
,
i
= …
,-
2
,-
1
,
0
,
1
,
2
,
…, is an identification function, θ
i
is a strictly ordered sequence of real numbers, unbounded on the left and on the right,
pj
,
j
= 1
,
2
,
…
,m,
are fixed integers, and the linear homogeneous system associated with (7.1) satisfies exponential dichotomy. The problem of the existence is studied without any sign condition on deviations of the argument.