On a nonlinear binomial equation of third order (Q1203059)

The author considers the nonlinear binomial differential equation of the third order (1) \(u'''+p(t)u^ \alpha=0\), where \(p\) is a continuous function on the interval \((a,\infty)\) with \(a>-\infty\), and \(\alpha>1\) is an odd integer. In the paper a necessary and sufficient condition for the solution of (1) \((p\leq 0\) on \((a,\infty))\) to be oscillatory and some sufficient conditions for the solution of (1) in the case \(p\leq 0\) and \(p\geq 0\) to be oscillatory or nonoscillatory are derived. For this, methods and results of the theory of linear differential equations of the third order are effectively used.