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Cím:On small solutions to second-order linear differential equations with nonmonotonous random coefficients.
Szerző:Hatvani, L\'aszl\'a
Forrás:Acta Sci. Math. 68, No.3-4, 705-725 (2002)
Nyelv:English
Absztrakt:Here, the second-order linear differential equation $x^{''}+a^2(t)x=0$ is considered with $a(t):=a_k$, if $t_{k-1}\le t \le t_{k}$. The sequence $\{a_k\}_{k=1}^{k=\infty}$ ($a_k >0$) is given and it is assumed that the numbers $t_k-t_{k-1}$ are totally independent random variables uniformly distributed on the interval $[0,1]$. The problem was studied for monotone step functions. The author gives conditions under which the same properties of the solution are preserved in case of nonmonotonous step functions.} \RV{Istv\'an Farag\'o (Budapest) 
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