Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $a(t)=\exp\{-2 \int^t f(s)\,ds\}$.

References [Enhancements On Off] (What's this?)

  • 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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34C10

Retrieve articles in all journals with MSC (1991): 34C10

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

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

American Mathematical Society