The property (A) for a certain class of the third order ODE

Kováčová, Monika

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New results on the nonoscillation of solutions of some nonlinear differential equations of third order.

Tunç, Ercan (2009)

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A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations

Ondřej Došlý, Jaroslav Jaroš (2003)

Archivum Mathematicum

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

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We discuss an open question of Kiguradze and Chanturia about Property $A$ and Property $B$ for the equation $y^{(n)} + p y = 0$ . The proposed integral criterion is proved in a few cases.

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