Analytic solutions of general nonlinear functional equations near resonance
The method of majorant series is used to find the unique solution \(\varphi:\mathbb C \to\mathbb C\) which is analytic in a neighborhood of the origin of a \(q\)-difference-type functional equation of infinite order (with inner linear functions having different coefficients \(q_j\)). Applications to \(q\)-difference equations (special cases of those considered in the paper, with \(q_j = q^j\)) as well as to functional equations with iterates of the unknown function are discussed. Results obtained by \textit{E. N. Petropoulou} and \textit{P. D. Siafarikas} [J. Math. Anal. Appl. 279, No. 2, 451--462 (2003; Zbl 1021.39011)] for another special case of the authors' equation are commented and sometimes corrected.
scientific article; zbMATH DE number 5017404