Formal asymptotics of solutions to certain linear differential equations involving oscillation


Let denote the ring of analytic -periodic functions in on the real axis. Let denote the ring of formal Laurent series in , whose coefficients are defined on a common strip neighbourhood of the real axis. In this paper, we study the linear differential equation

with coefficients in . We prove that, after a change of variables with and , this equation admits a basis of formal solutions of the form

where , and . This generalizes a well known result when is replaced by .

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