Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations
Archivum mathematicum, Tome 38 (2002) no. 4, pp. 311-317
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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 $.
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 $.
Classification :
34C10, 34D05
Keywords: the fourth order differential equation; nonoscillatory solution
Keywords: the fourth order differential equation; nonoscillatory solution
@article{ARM_2002_38_4_a7,
author = {Sobalov\'a, Monika},
title = {Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations},
journal = {Archivum mathematicum},
pages = {311--317},
year = {2002},
volume = {38},
number = {4},
mrnumber = {1942661},
zbl = {1090.34028},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a7/}
}
Sobalová, Monika. Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations. Archivum mathematicum, Tome 38 (2002) no. 4, pp. 311-317. http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a7/