Geodesic
Riccati equation and linear oscillators of variable frequency
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 159-162 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : explicit construction of a support solution. 
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     author = {V. V. Ivanov},
     title = {Riccati equation and linear oscillators of variable frequency},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2011_8_a12/}
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V. V. Ivanov. Riccati equation and linear oscillators of variable frequency. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 159-162. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a12/

[1] F. Khartman, Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[2] A. Wintner, “A criterion of oscillatory stability”, Quart. Appl. Math., 7:1 (1949), 115–117 | MR | Zbl

[3] I. V. Kamenev, “Ob odnom integralnom priznake koleblemosti lineinykh differentsialnykh uravnenii vtorogo poryadka”, Matem. zametki, 23:2 (1978), 249–252 | MR | Zbl