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Nonlinear criteria for the existence of the exponential trichotomy in infinite dimensional spaces

✍ Scribed by Bogdan Sasu; Adina Luminiţa Sasu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
289 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper we obtain for the first time nonlinear conditions for the existence of the exponential trichotomy of skew-product flows in infinite dimensional spaces. We treat the most general case without any additional assumptions concerning the cocycle and without assuming a priori the existence of the projection families. We show that an inedit assembly of integral conditions imply the existence of the exponential trichotomy with all of its properties and we prove that the imposed conditions are also necessary. Our results generalize the previous studies on this topic and provide as particular cases many interesting situations, among which we mention the detection of the exponential trichotomy of general non-autonomous systems.

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