On Expansions of Solutions of Riccati's Equation in Asymptotic Series

V. S. Samovol

National Research University "Higher School of Economics", Moscow

Abstract: We consider scalar real Riccati equations with coefficients expanding in convergent power series in a neighborhood of infinity. Continued solutions of such equations are studied. Power geometry methods are used to obtain conditions for expanding these solutions in asymptotic series.

Keywords: Riccati equation, extended solution, power geometry, Newton polygon, asymptotic series.

UDC: 517.91

Received: 23.01.2020

DOI: 10.4213/mzm12681

 English version: Mathematical Notes, 2021, 110:1, 135–144

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