Geodesic
On the Theory of Differential Equations with Random Coenfficients
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 309-318 
G. Ya. Lyubarskii; Yu. L. Rabotnikov. On the Theory of Differential Equations with Random Coenfficients. Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 309-318. http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a6/
@article{TVP_1963_8_3_a6,
     author = {G. Ya. Lyubarskii and Yu. L. Rabotnikov},
     title = {On the {Theory} of {Differential} {Equations} with {Random} {Coenfficients}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {309--318},
     year = {1963},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The equation $\ddot u(t)+a_1(t)\dot u(t)+[\alpha(t)-\alpha(t)]u(t)=0$ is considered where the coefficient $a_1(t)$ and $a_0 (t)$ are real, piecewise continuous and periodic functions with the same period $T$ and $\alpha (t)$ is a real random function. The restrictions on the $\alpha (t)$ are essentially the following. The correlation length $\alpha $ is much shorter than the period $T$, the random function $\alpha(t)$, $\infty, does not exceed the value ${\gamma/{\sqrt a(\gamma={\text{const}}<1)}}$. The necessary and sufficient conditions are found for the boundedness of mean values $Mu^2 (t),M[u(t)\dot u(t)]$ and $M\dot u^2 (t)$.