q-Nagumo norms and formal solutions to singularly perturbed q-difference equations
摘要
The aim of this work is to establish the existence, uniqueness and q-Gevrey character of formal power series solutions of q-analogues of analytic doubly-singular equations. Using a new family of norms adapted to q-differences we find new types of optimal divergence associated with these problems. We also provide some examples to illustrate our results.