Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 153, pp. 1-13.
Psi-exponential dichotomy for linear differential equations in a Banach space
Atanaska Georgieva, Hristo Kiskinov, Stepan Kostadinov, Andrey Zahariev
Abstract:
In this article we extend the concept psi-exponential and
psi-ordinary dichotomies for homogeneous linear differential
equations in a Banach space. With these two concepts we prove the
existence of psi-bounded solutions of the appropriate inhomogeneous
equation. A roughness of the psi-dichotomy is also considered.
Submitted March 28, 2013. Published July 2, 2013.
Math Subject Classifications: 34G10, 34D09, 34C11.
Key Words: Dichotomy for ordinary differential equations;
psi-dichotomy; psi-boundedness; psi-stability.
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Atanaska Georgieva
Faculty of Mathematics and Informatics,
University of Plovdiv
236 Bulgaria Blvd., 4003 Plovdiv, Bulgaria
email: atanaska@uni-plovdiv.bg
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Hristo Kiskinov
Faculty of Mathematics and Informatics,
University of Plovdiv
236 Bulgaria Blvd., 4003 Plovdiv, Bulgaria
email: kiskinov@uni-plovdiv.bg
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Stepan Kostadinov
Faculty of Mathematics and Informatics,
University of Plovdiv
236 Bulgaria Blvd., 4003 Plovdiv, Bulgaria
email: stkostadinov@uni-plovdiv.bg
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Andrey Zahariev
Faculty of Mathematics and Informatics,
University of Plovdiv
236 Bulgaria Blvd., 4003 Plovdiv, Bulgaria
email: zandrey@uni-plovdiv.bg
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