Asymptotic existence theorem for formal power series solutions of singularly perturbed linear q-difference equations.

Tahara, Hidetoshi

Let q > 1. In this paper, we consider a system of singularly perturbed linear holomorphic q-difference equations with a small parameter. This system has a formal power series solution with respect to the parameter with holomorphic coefficients such that the domain of coefficients becomes progressively smaller. The purpose of this paper is to construct a true holomorphic solution of the system that admits this formal power series solution as an asymptotic expansion with respect to the parameter.

EXISTENCE theorems; LINEAR equations; EQUATIONS

Mathematische Annalen, 2024, Vol 390, Issue 3, p3995

0025-5831

Academic Journal

10.1007/s00208-024-02861-5