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The exact region of oscillation for a first order neutral differential equation with delays
Author(s):
Sui
Sun
Cheng;
Yi-zhong
Lin
Journal:
Quart. Appl. Math.
64
(2006),
433-445.
MSC (2000):
Primary 34C10
Posted:
June 13, 2006
MathSciNet review:
2259047
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Abstract:
The theory of envelopes is applied to yield the exact geometric region of oscillation for a class of first order neutral differential equation with delays. As examples, we show that the convex region of oscillation yield oscillation criteria that are sharp.
References:
-
- 1.
- H. S. Ren and Z. X. Zheng, The algebraic criteria of oscillation of linear neutral differential equations with delays, J. Biomath., 13(1)(1998), 43-46 (in Chinese). MR 1845813 (2002b:34107)
- 2.
- H. S. Ren, On the accurate distribution of characteristic roots and stability of linear delay differential systems, Northeastern Forestry University Press, Harbin, 1999 (in Chinese).
- 3.
- S. S. Cheng and Y. Z. Lin, Exact regions of oscillation for a neutral differential equation, Proc. Royal Soc. Edin., 130A(2000), 277-286. MR 1750831 (2001k:34125)
- 4.
- V. G. Boltyanskii, Envelopes, Popular Lectures in Mathematics, Vol. 12, Macmillan Company, New York, 1964.
- 5.
- S. Z. Lin, Oscillation in first order neutral differential equations, Ann. Diff. Eqs., 19(3)(2003), 334-336. MR 2018300 (2005g:34159)
- 6.
- I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Science Publications, Clarendon Press, Oxford, 1991. MR 1168471 (93m:34109)
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Additional Information:
Sui
Sun
Cheng
Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
Yi-zhong
Lin
Affiliation:
Department of Mathematics, Fujian Normal University, Fuzhou, Fujian 350007, People's Republic of China
PII:
S0033-569X-06-01013-2
Received by editor(s):
March 11, 2005
Posted:
June 13, 2006
Copyright of article:
Copyright
2006,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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