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On the solutions of ordinary differential equations in the form of Dulac series

Qualitative Theory of Dynamical Systems. 2022. Vol. 21. Article 47.
V. S. Samovol

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.

Research target: Mathematics
Language: English
Full text
DOI
Text on another site
Keywords: Newton polygonformal solutionConvergenceСontinuable solutionDulac series
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