Properties of bounded solutions of nonlinear equations of second order.

Here we consider only solutions of (E) which are defined on some ray [c, + oo ), c _ 0 (depending on the particular solution), and their existence will be assumed without further mention. An oscillatory solution x(t), tE [c, + X ) of (E), is (by definition) a solution such that for any t > c, there exists a t1 > t with x(ti) = 0. In the first section we give a theorem in which f (t) is allowed to be negative part of the time, and in the second section we give a criterion in order that all bounded solutions of (E) oscillate.