Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations

Sobalová, Monika. "Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations." Archivum Mathematicum 038.4 (2002): 311-317. <http://eudml.org/doc/248928>.

@article{Sobalová2002,
abstract = {In the paper the fourth order nonlinear differential equation $y^\{(4)\}+(q(t)y^\{\prime \})^\{\prime \}+r(t)f(y)=0$, where $q\in C^\{1\}( [0,\infty ))$, $r\in C^\{0\}( [0,\infty ))$, $f\in C^\{0\}(R)$, $r\ge 0$ and $f(x)x>0$ for $x\ne 0$ is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for $t\rightarrow \infty $.},
author = {Sobalová, Monika},
journal = {Archivum Mathematicum},
keywords = {the fourth order differential equation; nonoscillatory solution; fourth order differential equation; nonoscillatory solution},
language = {eng},
number = {4},
pages = {311-317},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations},
url = {http://eudml.org/doc/248928},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Sobalová, Monika
TI - Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 4
SP - 311
EP - 317
AB - In the paper the fourth order nonlinear differential equation $y^{(4)}+(q(t)y^{\prime })^{\prime }+r(t)f(y)=0$, where $q\in C^{1}( [0,\infty ))$, $r\in C^{0}( [0,\infty ))$, $f\in C^{0}(R)$, $r\ge 0$ and $f(x)x>0$ for $x\ne 0$ is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for $t\rightarrow \infty $.
LA - eng
KW - the fourth order differential equation; nonoscillatory solution; fourth order differential equation; nonoscillatory solution
UR - http://eudml.org/doc/248928
ER -