Riccati equation and linear oscillators of variable frequency

V. V. Ivanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

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.

UDC: 517.926

MSC: 34C10

Received July 6, 2011, published July 14, 2011