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Natural Boundaries for Solutions to a Certain Class of Functional Differential Equations

โœ Scribed by J.C. Marshall; B. van Brunt; G.C. Wake

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
222 KB
Volume
268
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

This paper is concerned with a generalization of a functional differential equation known as the pantograph equation. The pantograph equation contains a linear functional argument. In this paper we generalize this functional argument to include nonlinear polynomials. In contrast to the entire solutions generated by the pantograph equation for the retarded case, we show that in the nonlinear case natural boundaries occur. These boundaries are linked to the Julia set of the polynomial functional argument. ๏ฃฉ 2002 Elsevier Science (USA)

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