Analytic solutions of general nonlinear functional equations near resonance

DOI10.1016/j.jmaa.2005.05.037zbMath1149.39014OpenAlexW2037360850MaRDI QIDQ820046

Bing Xu, Wei Nian Zhang

Publication date: 6 April 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.05.037

zbMATH Keywords

\(q\)-difference equationsiterative functional equationsanalytic solutionsmajorant seriesDiophantine conditionfunctional equations of infinite order

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Difference equations, scaling ((q)-differences) (39A13) Functional equations for complex functions (39B32)

Related Items (7)

Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin ⋮ Formal solutions of the generalized Dhombres functional equation with value one at zero ⋮ Analytic invariant curves for a planar mapping ⋮ Existence of analytic solutions of an iterative functional equation ⋮ Small divisor problem for an analytic \(q\)-difference equation ⋮ Analytic solutions of an iterative differential equation under Brjuno condition ⋮ Analytic solutions of a second-order functional differential equation

Cites Work

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• Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles
• Existence and uniqueness of solutions in \(H_{1}(\Delta)\) of a general class of non-linear functional equations
• ANALYTIC SOLUTIONS OF A POLYNOMIAL-LIKE ITERATIVE FUNCTIONAL EQUATION
• Invariant curves for planar mappings
• Solutions of equivariance for a polynomial-like iterative equation
• Analytic Solutions of aq-Difference Equation and Applications to Iterative Equations^*
• Discussion on the differentiable solutions of the iterated equation
• Analytic solutions of a functional equation for invariant curves

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