Existence of analytic solutions to analytic nonlinear q-difference equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Li, Xianyi¹  Zhang, Changgui² 

[1] Shenzhen Univ, Coll Math & Computat Sci, Shenzhen 518060, Guangdong, Peoples R China

[2] Univ Lille 1, Lab P Painleve, UFR Math, F-59655 Villeneuve Dascq, France

关键词: Difference equation;    Analytic solution;    Isomorphism;    Diffeomorphism;    Newton's polygon;    Poincare domain;   

DOI  :  10.1016/j.jmaa.2010.09.035

来源: Elsevier

【 摘 要 】

In this paper, some analytic approaches are formulated for the existence of analytic solutions of analytic nonlinear difference equations. From the point of view of dynamical systems, analytic solutions of such kinds of equations can be generally expressed by formal power series of exponential variables, so we are interested in considering a difference equation as a q-difference equation via a suitable coordinate transformation. After stating analytic results for formal series solutions of nonlinear q-difference equations, we also derive some results for the existence of analytic solutions to autonomous rational difference equations. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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