On small solutions of second order differential equations with random coefficients
Archivum Mathematicum (1998)
- Volume: 034, Issue: 1, page 119-126
- ISSN: 0044-8753
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topHatvani, László, and Stachó, László. "On small solutions of second order differential equations with random coefficients." Archivum Mathematicum 034.1 (1998): 119-126. <http://eudml.org/doc/248216>.
@article{Hatvani1998,
abstract = {We consider the equation \[x^\{\prime \prime \}+a^2(t)x=0,\qquad a(t):=a\_k\ \hbox\{ if \}t\_\{k-1\}\le t<t\_k,\ \hbox\{ for \}k=1,2,\ldots ,\]
where $\lbrace a_k\rbrace $ is a given increasing sequence of positive numbers, and $\lbrace t_k\rbrace $ is chosen at random so that $\lbrace t_k-t_\{k-1\}\rbrace $ are totally independent random variables uniformly distributed on interval $[0,1]$. We determine the probability of the event that all solutions of the equation tend to zero as $t\rightarrow \infty $.},
author = {Hatvani, László, Stachó, László},
journal = {Archivum Mathematicum},
keywords = {Asymptotic stability; energy method; small solution; asymptotic stability; energy method; small solution},
language = {eng},
number = {1},
pages = {119-126},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On small solutions of second order differential equations with random coefficients},
url = {http://eudml.org/doc/248216},
volume = {034},
year = {1998},
}
TY - JOUR
AU - Hatvani, László
AU - Stachó, László
TI - On small solutions of second order differential equations with random coefficients
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 1
SP - 119
EP - 126
AB - We consider the equation \[x^{\prime \prime }+a^2(t)x=0,\qquad a(t):=a_k\ \hbox{ if }t_{k-1}\le t<t_k,\ \hbox{ for }k=1,2,\ldots ,\]
where $\lbrace a_k\rbrace $ is a given increasing sequence of positive numbers, and $\lbrace t_k\rbrace $ is chosen at random so that $\lbrace t_k-t_{k-1}\rbrace $ are totally independent random variables uniformly distributed on interval $[0,1]$. We determine the probability of the event that all solutions of the equation tend to zero as $t\rightarrow \infty $.
LA - eng
KW - Asymptotic stability; energy method; small solution; asymptotic stability; energy method; small solution
UR - http://eudml.org/doc/248216
ER -
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