An invariant manifold of slowly oscillating solutions for x(t) = - ...x(t) + f(x(t-1)).
A second-order half-linear ordinary differential equation of the type is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.
In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for must be unbounded, provided , in and for every bounded subset , is bounded in . (B) Every bounded solution for , in , must be constant, provided in and for every bounded subset , is bounded in .