Analytic Solutions of an Iterative Functional Differential Equation near Resonance. (22nd April 2009)

• Record Type: Journal Article
• Authors: Liu, Tongbo; Li, Hong
• Other Names: Wang Peiguang Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2009(2009)
• Publication Date: 2009-04-22
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2009/145213
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown functionx ′′ ( z ) + c x ′ ( z ) = x ( a z + b x ( z ) ) in the complex fieldℂ . By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown functionλ 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.