This article is cited in 19 papers

Two comparison criteria for scalar Riccati equations and their applications

G. A. Grigoryan

Institute of Mathematics, National Academy of Sciences, Republic of Armeniya, Erevan, Republic of Armeniya

Abstract: We establish two comparison criteria for scalar Riccati equations. On the base of these criteria we prove two coefficient criteria for the existence of solutions to Riccati equations (both tending to infinity and not). We generalize a part of the Lyapunov theorem on the Hill equation and establish solvability criteria for the Redheffer system.

Keywords: Riccati, Hill, Matheus equations, Redheffer system, comparison criteria, dissipativity, conservativity, $p$-dissipativity, $p$-conservativity.

UDC: 517.923

Received: 20.09.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:11, 17–30

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