Integral averages and oscillation of second order sublinear differential equations

Manojlović, Jelena V.. "Integral averages and oscillation of second order sublinear differential equations." Czechoslovak Mathematical Journal 55.1 (2005): 41-60. <http://eudml.org/doc/30926>.

@article{Manojlović2005,
abstract = {New oscillation criteria are given for the second order sublinear differential equation \[ [a(t)\psi (x(t))x^\{\prime \}(t)]^\{\prime \}+q(t)f(x(t))=0, \quad t\ge t\_0>0, \] where $a\in C^1([t_0,\infty ))$ is a nonnegative function, $\psi , f\in C(\{\mathbb \{R\}\})$ with $\psi (x)\ne 0$, $xf(x)/\psi (x)>0$ for $x\ne 0$, $\psi $, $f$ have continuous derivative on $\{\mathbb \{R\}\}\setminus \lbrace 0\rbrace $ with $[f(x)/\psi (x)]^\{\prime \}\ge 0$ for $x\ne 0$ and $q\in C([t_0,\infty ))$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^\{\prime \prime \}(t)+q(t)x(t)=0$.},
author = {Manojlović, Jelena V.},
journal = {Czechoslovak Mathematical Journal},
keywords = {oscillation; sublinear differential equation; integral averages; oscillation; sublinear differential equation; integral averages},
language = {eng},
number = {1},
pages = {41-60},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Integral averages and oscillation of second order sublinear differential equations},
url = {http://eudml.org/doc/30926},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Manojlović, Jelena V.
TI - Integral averages and oscillation of second order sublinear differential equations
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 41
EP - 60
AB - New oscillation criteria are given for the second order sublinear differential equation \[ [a(t)\psi (x(t))x^{\prime }(t)]^{\prime }+q(t)f(x(t))=0, \quad t\ge t_0>0, \] where $a\in C^1([t_0,\infty ))$ is a nonnegative function, $\psi , f\in C({\mathbb {R}})$ with $\psi (x)\ne 0$, $xf(x)/\psi (x)>0$ for $x\ne 0$, $\psi $, $f$ have continuous derivative on ${\mathbb {R}}\setminus \lbrace 0\rbrace $ with $[f(x)/\psi (x)]^{\prime }\ge 0$ for $x\ne 0$ and $q\in C([t_0,\infty ))$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^{\prime \prime }(t)+q(t)x(t)=0$.
LA - eng
KW - oscillation; sublinear differential equation; integral averages; oscillation; sublinear differential equation; integral averages
UR - http://eudml.org/doc/30926
ER -