Electron. J. Diff. Eqns., Vol. 2009(2009), No. 51, pp. 1-8.

Analytic solutions of a first order functional differential equation with a state derivative dependent delay

Pingping Zhang

Abstract:
This article concerns the first-order functional differential equation
$$ x'(z)=x(p(z)+bx'(z)) $$
with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

Submitted September 25, 2008. Published April 13, 2009.
Math Subject Classifications: 34K05, 34A25, 39B32.
Key Words: Functional differential equation; analytic solution.

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Pingping Zhang
Department of Mathematics, Binzhou University
Shandong 256603, China
email: zhangpingpingmath@163.com

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