IJPAM: Volume 73, No. 3 (2011)

GENERALIZED DICHOTOMY FOR ORDINARY
DIFFERENTIAL EQUATIONS IN A BANACH SPACE

A. Georgieva$^1$, H. Kiskinov$^2$
$^{1,2}$Faculty of Mathematics and Informatics
University of Plovdiv
236, Bulgaria Blvd., Plovdiv, 4003, BULGARIA


Abstract. A dichotomy similar property for a class of homogeneous differential equations in an arbitrary Banach space is introduced. By help of them, existence of quasi bounded solutions of the appropriate nonhomogeneous equation is proved. A special roughness for such equations is considered.

Received: November 7, 2011

AMS Subject Classification: 34G10, 34G20

Key Words and Phrases: ordinary differential equations, generalized dichotomy

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 3