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 | 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.**Ralph Byers, B. J. Harris, and Man Kam Kwong,*Weighted means and oscillation conditions for second order matrix differential equations*, J. Differential Equations**61**(1986), no. 2, 164–177. MR**823400**, 10.1016/0022-0396(86)90117-8**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), no. 1, 263–282. MR**896022**, 10.1090/S0002-9947-1987-0896022-5**3.**Lynn H. Erbe, Qingkai Kong, and Shi Gui Ruan,*Kamenev type theorems for second-order matrix differential systems*, Proc. Amer. Math. Soc.**117**(1993), no. 4, 957–962. MR**1154244**, 10.1090/S0002-9939-1993-1154244-0**4.**G. H. Hardy, J. E. Littlewood, and G. Pólya,*Inequalities*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988. Reprint of the 1952 edition. MR**944909****5.**I. V. Kamenev,*An integral test for conjugacy for second order linear differential equations*, Mat. Zametki**23**(1978), no. 2, 249–251 (Russian). MR**0486798****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:
http://dx.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