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On the Solutions of Ordinary Differential Equations in the Form of Dulac Series

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We consider a nonlinear ordinary differential equation of arbitrary order with coefficients in the form of power series that converge in a neighborhood of the origin. The methods created in power geometry in recent years make it possible to compute formal solutions to that equation in the form of Dulac series. We describe the corresponding algorithm and prove a sufficient convergence condition for such formal solutions.

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Samovol, V.S. On the Solutions of Ordinary Differential Equations in the Form of Dulac Series. Qual. Theory Dyn. Syst. 21, 47 (2022).

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