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

DOI:
https://doi.org/10.1090/S0002-9939-98-04248-8

MathSciNet review:
1443844

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Abstract | References | Similar Articles | Additional Information

Abstract: Some oscillation criteria are given for the second order matrix differential system , where and are real continuous matrix functions with symmetric, . These results improve oscillation criteria recently discovered by Erbe, Kong and Ruan by using a generalized Riccati transformation , where is the identity matrix, is a given function on and .

**1.**R. Byers, B. J. Harris and M. K. Kwong,*Weighted means and oscillation conditions for second order matrix differential equations*, J. Differential Equations**61**(1986), 164-177. MR**87f:34033****2.**G. J. Butler, L. H. Erbe and A. B. Mingarelli,*Riccati techniques and variational principles in oscillation theory for linear systems*, Trans. Amer. Math. Soc.**303**(1987), 263-282. MR**88h:34023****3.**L. H. Erbe, Q. Kong and S. Ruan,*Kamenev type theorems for second order matrix differential systems*, Proc. Amer. Math. Soc.**117**(1993), 957-962. MR**93e:34045****4.**G. H. Hardy, J. E. Littlewood and G. Pólya,*Inequalities*, 2nd ed., Cambridge Univ. Press, Cambridge, UK, 1988. MR**89d:26016****5.**I. V. Kamenev,*An integral criterion for oscillation of linear differential equations of second order*, Mat. Zametki**23**(1978), 249-251. MR**58:6497****6.**Fanwei Meng,*Oscillation of second order matrix differential systems*, Advances in Mathematics (Chinese), 24.4 (1995), 370-372.

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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:
https://doi.org/10.1090/S0002-9939-98-04248-8

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