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Zbl 1164.34025
Boichuk, Alexander; Pokutnyi, Alexander
Bounded solutions of linear perturbed differential equations in a Banach space.
(English)
[J] Tatra Mt. Math. Publ. 38, 29-40 (2007). ISSN 1210-3195

The linear weakly perturbed differential equation $$\dot x=A(t)x+\varepsilon A_1(t)x+f(t)$$ in Banach spaces is studied for $t\in \Bbb R$ by supposing that $\dot x=A(t)x$ has exponential dichotomies on both semi-axes $\Bbb R_\pm$. Conditions on the existence of bounded solutions on $\Bbb R$ of the above weakly perturbed equation are established. Concrete examples are presented at the end of the paper.
[Michal Fečkan (Bratislava)]
MSC 2000:
*34G10 Linear ODE in abstract spaces
34C11 Qualitative theory of solutions of ODE: Growth, etc.
34D09 Dichotomy, trichotomy

Keywords: exponential dichotomies; generalized inverse operator; Fredholm operator

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