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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2011, Volume 8, Pages 159–162 (Mi semr312)  
Riccati equation and linear oscillators of variable frequency

V. V. Ivanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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Abstract: The necessary and sufficient conditions are presented for oscillability of the equation $\ddot x+\omega^2x=0$ with variable coefficient $\omega$.
Keywords: linear ocsillators of variable frequency, Riccati's equation and oscillability of linear systems, integral conditions of Wintner and Kamenev, explicit construction of a support solution.
Received July 6, 2011, published July 14, 2011
Document Type: Article
UDC: 517.926
MSC: 34C10
Language: Russian
Citation: V. V. Ivanov, “Riccati equation and linear oscillators of variable frequency”, Sib. Èlektron. Mat. Izv., 8 (2011), 159–162
Citation in format AMSBIB
\Bibitem{Iva11}
\by V.~V.~Ivanov
\paper Riccati equation and linear oscillators of variable frequency
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 159--162
\mathnet{http://mi.mathnet.ru/semr312}
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