Oscillations results for Emden-Fowler type differential equations

The third order nonlinear differential equation (*) x''' + a(t)x' + b(t)f(x) = 0 is considered. We present oscillation and nonoscillation criteria which extend and improve previous results existing in the literature, in particular some results recently stated by M. Gregus and M. Gregus, Jr., (J. Math. Anal. Appl. 181, 1994, 575-585). In addition, contributions to the classification of solutions are given. The techniques used are based on a transformation which reduces (*) to a suitable disconjugate form. To this aim auxiliary results on the asymptotic behavior of solutions of a second order linear differential equation associated to (*) are stated. They are presented in an independent form because they may be applied also to simplify and improve other qualitative problems concerning differential equations with quasiderivatives.