On the sharpness of a theorem by cooke and Verduyn Lunel

Kenneth L. Cooke; Gregory Derfel

doi:10.1006/jmaa.1996.0026

On the sharpness of a theorem by cooke and Verduyn Lunel

Kenneth L. Cooke, Gregory Derfel

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The sharpness of a theorem of K. Cooke and S. M. Verduyn Lunel (Differential Integral Equations 6 (1993) 1101-1117) about small solutions of linear time-dependent delay equations is proved. A wide class of nonautonomous functional-differential equations possessing small solutions is constructed. The construction is based on the existence of quickly decreasing solutions of functional-differential equations with linearly expanded arguments.

Original language	English
Pages (from-to)	379-391
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	197
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.1996.0026
State	Published - 1 Jan 1996

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "On the sharpness of a theorem by cooke and Verduyn Lunel",

abstract = "The sharpness of a theorem of K. Cooke and S. M. Verduyn Lunel (Differential Integral Equations 6 (1993) 1101-1117) about small solutions of linear time-dependent delay equations is proved. A wide class of nonautonomous functional-differential equations possessing small solutions is constructed. The construction is based on the existence of quickly decreasing solutions of functional-differential equations with linearly expanded arguments.",

author = "Cooke, {Kenneth L.} and Gregory Derfel",

note = "Funding Information: The research of the first author is partially supported by a grant from the U.S. National Science Foundation. The research of the second author is supported in part by a grant of the Israel Ministry of Science and by a grant of the Israel Academy of Science and Humanities. Remark 2 in the paper was stimulated by a comment of Wenzhang Huang. One of us G. D.) thanks A. D. Myshkis for fruitful discussions and for reading the manuscript.",

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AU - Derfel, Gregory

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N2 - The sharpness of a theorem of K. Cooke and S. M. Verduyn Lunel (Differential Integral Equations 6 (1993) 1101-1117) about small solutions of linear time-dependent delay equations is proved. A wide class of nonautonomous functional-differential equations possessing small solutions is constructed. The construction is based on the existence of quickly decreasing solutions of functional-differential equations with linearly expanded arguments.

AB - The sharpness of a theorem of K. Cooke and S. M. Verduyn Lunel (Differential Integral Equations 6 (1993) 1101-1117) about small solutions of linear time-dependent delay equations is proved. A wide class of nonautonomous functional-differential equations possessing small solutions is constructed. The construction is based on the existence of quickly decreasing solutions of functional-differential equations with linearly expanded arguments.

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ER -

On the sharpness of a theorem by cooke and Verduyn Lunel

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