On a Nonlinear Binomial Equation of Third Order

Abstract

A necessary and sufficient condition for the solution of equation $u^{\prime \prime \prime }+p(t)u^{\alpha }=0(\alpha >0$ an odd integer, $p\le 0$ on $(a,\infty ))$ to be oscillatory and some sufficient conditions for the solution in the cases $p\le 0$ and $p\ge 0$ to be oscillatory or non-oscillatory are derived. For this methods and results of the theory of linear differential equations of the third order are effectively used.