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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
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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:

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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)

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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).

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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)

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V. G. Boltyanskii, Envelopes, Popular Lectures in Mathematics, Vol. 12, Macmillan Company, New York, 1964.

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S. Z. Lin, Oscillation in first order neutral differential equations, Ann. Diff. Eqs., 19(3)(2003), 334-336. MR 2018300 (2005g:34159)

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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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