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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fixed points and stability in neutral differential equations with variable delays


Authors: Chuhua Jin and Jiaowan Luo
Journal: Proc. Amer. Math. Soc. 136 (2008), 909-918
MSC (2000): Primary 34K20, 34K40
Published electronically: November 30, 2007
MathSciNet review: 2361863
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider a linear scalar neutral delay differential equation with variable delays and give some new conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results of Burton, Raffoul, and Zhang are improved and generalized.


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Additional Information

Chuhua Jin
Affiliation: Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong 510090, People’s Republic of China
Email: jinchuhua@tom.com

Jiaowan Luo
Affiliation: Corresponding author. School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, People’s Republic of China
Email: mathluo@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09089-2
PII: S 0002-9939(07)09089-2
Keywords: Fixed points, stability, neutral delay differential equations, variable delays.
Received by editor(s): October 10, 2006
Published electronically: November 30, 2007
Additional Notes: The second author was supported in part by NNSF of China Grant #10671043.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.