On some classes of solutions of a nonlinear second order neutral delay differential equation.

摘要

The authors consider the neutral delay differential equation (p(t)(x(t)+h(t)x(t-η))')'+q(t)f(x(t-σ))=0,t≥t_o (*) were p,h,q∈c([t_o,∞],R), η and σ are nonnegative real numbers and f:R→R is continuously differentiable such that uf(u)>0 for u≠0. Dividing the solutions of (into four classes, the authors obtain conditions for the existence of solutions in these classes.