Geodesic
Two comparison criteria for scalar Riccati equations and their applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2012), pp. 20-35

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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, Redheffer system, comparison criteria, dissipativity, conservativity, $p$-dissipativity, $p$-conservativity.
Mots-clés : Matheus equations 
@article{IVM_2012_11_a1,
     author = {G. A. Grigoryan},
     title = {Two comparison criteria for scalar {Riccati} equations and their applications},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {20--35},
     publisher = {mathdoc},
     number = {11},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_11_a1/}
}
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G. A. Grigoryan. Two comparison criteria for scalar Riccati equations and their applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2012), pp. 20-35. http://geodesic.mathdoc.fr/item/IVM_2012_11_a1/