This article is cited in 1 paper

On extensibility and qualitative properties of solutions to Riccati's equation

I. V. Astashova^ab, V. A. Nikishov<sup>a

a</sup> Lomonosov Moscow State University
^b Plekhanov Russian State University of Economics

Abstract: We consider Riccati's equation on the real axis with continuous coefficients and non-negative discriminant of the right-hand side. We study the extensibility of its solutions to unbounded intervals. We obtain asymptotic formulae for its solutions in their dependence on the initial values and the properties of the functions representing roots of the right-hand side of the equation. We obtain results on the asymptotical behaviour of solutions defined near $\pm\infty$. We study the structure of the set of bounded solutions in the case when the roots of the right-hand side of the equation are $C^1$-functions which are different on the whole of their domain and tend monotonically to some limits as $x\to\pm\infty$. We extend, improve, or refine some well-known results.
Bibliography: 47 titles.

Keywords: Riccati's equation, non-negative discriminant, continuous coefficients, extensibility, qualitative properties, asymptotic properties.

UDC: 517.923

MSC: 34A34, 34D05

Received: 29.07.2023

DOI: 10.4213/rm10160

 English version: Russian Mathematical Surveys, 2024, 79:2, 189–227

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