Geodesic
Integral averages and oscillation of second order sublinear differential equations
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 41-60 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $x^{\prime \prime }(t)+q(t)x(t)=0$.
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 $x^{\prime \prime }(t)+q(t)x(t)=0$.
Classification : 34C10, 34C15, 34C29
Keywords: oscillation; sublinear differential equation; integral averages 
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     author = {Manojlovi\'c, Jelena V.},
     title = {Integral averages and oscillation of second order sublinear differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {41--60},
     year = {2005},
     volume = {55},
     number = {1},
     mrnumber = {2121655},
     zbl = {1081.34032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a2/}
}
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Manojlović, Jelena V. Integral averages and oscillation of second order sublinear differential equations. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 41-60. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a2/