A singular version of Leighton's comparison theorem for forced

quasilinear second order differential equations

Ondrej  Dosly, Jaroslav Jaros

Department of Mathematical Analysis,
Comenius University, Mlynska
Dolina,  842 15 Bratislava, Slovakia

E-mail:  dosly@math.muni.cz          jaros@alpha.dcs.fmph.uniba.sk
 
 
 

Abstract.
We extend the classical Leighton comparison theorem
to a class of quasilinear forced second order differential equations
$$
(r(t)|x'|^{\alpha-2}x')'+c(t)|x|^{\beta-2}x=f(t)\,,\quad
1<\alpha\leq \beta,\ t\in I=(a,b)\,,                              \tag{*}
$$
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.

AMSclassification.   34C10

Keywords.  Picone's identity, forced quasilinear equation, principal solution.