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Oscillatory behavior of linear matrix Hamiltonian systems

✍ Scribed by Yuan Gong Sun; Fanwei Meng

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
116 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We establish some new oscillation criteria for the matrix linear Hamiltonian system X β€² = A (t)X + B (t)Y, Y β€² = C (t)X –A *(t)Y by using a new function class X and monotone functionals on a suitable matrix space. In doing so, many existing results are generalized and improved. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A n y n q B n y g n is considered. The sequence of advances g n satisfies Ε½ . Ε½ . 1 F g n y n F N, where N is a fixed number. The matrices A n are invertible, Ε½ . whereas, in general, matrices B n are not. In this paper the notion of an ordinary dichotomy for a linear equation with advance is given