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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Oscillation of nonlinear systems of matrix differential equations

Author: A. G. Kartsatos
Journal: Proc. Amer. Math. Soc. 30 (1971), 97-101
MSC: Primary 34.42
MathSciNet review: 0280798
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Abstract: For systems of matrix equations of the form

$\displaystyle U' = A(t,U,V)V,\quad V' = - B(t,U,V)$

it is shown here that the oscillation problem can be reduced to the corresponding problem of ``associated'' (in some sense) scalar equations for which there exist numerous results. Furthermore, it is also shown that many of the existing results concerning the equation

$\displaystyle (A(t)U')' + B(t,U,U')U = 0$

can be considerably improved by application of the above method.

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Keywords: Nonlinear system of matrix differential equations, oscillatory system, oscillatory linear equation
Article copyright: © Copyright 1971 American Mathematical Society