Geodesic
A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations
Archivum mathematicum, Tome 39 (2003) no. 4, pp. 335-345.

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We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations \[ (r(t)|x^{\prime }|^{\alpha -2}x^{\prime })^{\prime }+c(t)|x|^{\beta -2}x=f(t)\,,\quad 1\alpha \le \beta ,\ t\in I=(a,b)\,, \qquad \mathrm {(*)}\] where the endpoints $a$, $b$ of the interval $I$ are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.
Classification : 34C10
Keywords: Picone’s identity; forced quasilinear equation; principal solution 
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     author = {Do\v{s}l\'y, Ond\v{r}ej and Jaro\v{s}, Jaroslav},
     title = {A singular version of {Leighton's} comparison theorem for forced quasilinear second order differential equations},
     journal = {Archivum mathematicum},
     pages = {335--345},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {2003},
     mrnumber = {2032106},
     zbl = {1116.34316},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2003__39_4_a8/}
}
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Došlý, Ondřej; Jaroš, Jaroslav. A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations. Archivum mathematicum, Tome 39 (2003) no. 4, pp. 335-345. http://geodesic.mathdoc.fr/item/ARM_2003__39_4_a8/