# zbMATH — the first resource for mathematics

On a theorem of Maillet-Malgrange type for $$q$$-differential-difference equations. (Sur un théorème du type de Maillet-Malgrange pour les équations $$q$$-différences-différentielles.) (French) Zbl 0938.34064
Summary: The growth of the coefficients of a formal power series satisfying a holomorphic $$q$$-difference differential equation is described, where differential and $$q$$-difference operators are mixed. Following an idea of B. Malgrange [Asympt. Anal. 2, No. 1, 1-4 (1989; Zbl 0693.34004)] and using the implicit function theorem, a generalization of the Maillet-Malgrange theorem is established.

##### MSC:
 34K12 Growth, boundedness, comparison of solutions to functional-differential equations 34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain 34K07 Theoretical approximation of solutions to functional-differential equations
ASYMPT