The exact region of oscillation for a first order neutral differential equation with delays
Authors:
Sui Sun Cheng and Yi-zhong Lin
Journal:
Quart. Appl. Math. 64 (2006), 433-445
MSC (2000):
Primary 34C10
DOI:
https://doi.org/10.1090/S0033-569X-06-01013-2
Published electronically:
June 13, 2006
MathSciNet review:
2259047
Full-text PDF Free Access
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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.
- Hong Shan Ren and Zu Xiu Zheng, The algebraic criteria of oscillation of linear neutral differential equations with delays, J. Biomath. 13 (1998), no. 1, 43–46 (Chinese, with English and Chinese summaries). MR 1845813
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).
- S. S. Cheng and Y. Z. Lin, Exact regions of oscillation for a neutral differential equation, Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), no. 2, 277–286. MR 1750831, DOI https://doi.org/10.1017/S0308210500000159
4 V. G. Boltyanskii, Envelopes, Popular Lectures in Mathematics, Vol. 12, Macmillan Company, New York, 1964.
- Shizhong Lin, Oscillation in first order neutral differential equations, Ann. Differential Equations 19 (2003), no. 3, 334–336. MR 2018300
- I. Győri and G. Ladas, Oscillation theory of delay differential equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. With applications; Oxford Science Publications. MR 1168471
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).
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.
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.
6 I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Science Publications, Clarendon Press, Oxford, 1991.
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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
Received by editor(s):
March 11, 2005
Published electronically:
June 13, 2006
Article copyright:
© Copyright 2006
Brown University
The copyright for this article reverts to public domain 28 years after publication.
