International Journal of Differential Equations

Analytic Solutions of an Iterative Functional Differential Equation near Resonance

Tongbo Liu and Hong Li

Full-text: Open access

Abstract

We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function x ′′ ( z ) + c x ( z ) = x ( a z + b x ( z ) ) in the complex field . By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function λ 2 g ′′ ( λ z ) g ( z ) λ g ( λ z ) g ′′ ( z ) + c ( g ( z ) ) 2 ( λ g ( λ z ) a g ( z ) ) = ( g ( z ) ) 3 ( g ( λ 2 z ) a g ( λ z ) ) , we get its local invertible analytic solutions.

Article information

Source
Int. J. Differ. Equ., Volume 2009 (2009), Article ID 145213, 14 pages.

Dates
Received: 6 January 2009
Accepted: 14 April 2009
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399813

Digital Object Identifier
doi:10.1155/2009/145213

Mathematical Reviews number (MathSciNet)
MR2525715

Zentralblatt MATH identifier
1207.34074

Citation

Liu, Tongbo; Li, Hong. Analytic Solutions of an Iterative Functional Differential Equation near Resonance. Int. J. Differ. Equ. 2009 (2009), Article ID 145213, 14 pages. doi:10.1155/2009/145213. https://projecteuclid.org/euclid.ijde/1485399813


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