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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
DOI: https://doi.org/10.1090/S0002-9939-1971-0280798-8
MathSciNet review: 0280798
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Abstract: For systems of matrix equations of the form \[ U’ = A(t,U,V)V,\quad V’ = - B(t,U,V)\] 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 \[ (A(t)U’)’ + B(t,U,U’)U = 0\] 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