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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Kamenev type theorems
for second order matrix differential systems


Authors: Fanwei Meng, Jizhong Wang and Zhaowen Zheng
Journal: Proc. Amer. Math. Soc. 126 (1998), 391-395
MSC (1991): Primary 34C10
MathSciNet review: 1443844
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Abstract: Some oscillation criteria are given for the second order matrix differential system $Y''+Q(t) Y=0$, where $Y$ and $Q$ are $n\times n$ real continuous matrix functions with $Q(t)$ symmetric, $t\in[t_0,\infty)$. These results improve oscillation criteria recently discovered by Erbe, Kong and Ruan by using a generalized Riccati transformation $V(t)=a(t)\{Y'(t) Y^{-1}(t) +f(t)I\}$, where $I$ is the $n\times n$ identity matrix, $f\in C^1$ is a given function on $[t_0,\infty)$ and $a(t)=\exp\{-2 \int^t f(s)\,ds\}$.


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Additional Information

Fanwei Meng
Affiliation: Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China

Jizhong Wang
Affiliation: Department of Mathematics, Linyi Teacher’s College, Linyi, Shandong, 276005, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04248-8
PII: S 0002-9939(98)04248-8
Keywords: Matrix differential system, oscillatory theory, Riccati equation
Received by editor(s): May 25, 1996
Additional Notes: The research is supported by the Natural Science Foundation of Shandong Province, P.R. China
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society