A classification scheme for positive solutions to second order nonlinear iterative differential equations.

Fan, Xianling; Li, Wan-Tong; Zhong, Chengkui

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Conjugacy criteria for half-linear differential equations

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Sufficient conditions on the function $c (t)$ ensuring that the half-linear second order differential equation $(| u^{'} |^{p - 2} u^{'})^{'} + c (t) {| u (t) |}^{p - 2} u (t) = 0, p > 1$ possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p = 2$ .

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