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Cím:On small solutions second-order differential equations with random coefficients.
Szerző:Hatvani, L\'aszl\'o; Stach\'o, L\'aszl\'o
Forrás:Arch. Math., Brno 34, No.1, 119-126 (1998). [ISSN 0044-8753; ISSN 1212-5059
Absztrakt:The authors pose the question: For arbitrarily fixed initial data, what is the probability, that the corresponding solution to the equation $$x''+a(t)x=0 \qquad t\geq 0,$$ vanishes at $+\infty $? The answer to this problem is given in the case when $a$ is a step function. More precisely, when $a(t)=a_k$ for $t_{k-1}\leq t<t_k$, $k=1,2, \dots $, $(a_k)_{k=1}^{+\infty }$ is a nondecreasing sequence of positive numbers and $t_k-t_{k-1}$, $k=1,2, \dots $ are independent random variables uniformly distributed on interval $[0,1]$.} \RV{A.Lomtatidze (Brno) 
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