Two classes of asymptotically different positive solutions of the equation y(t) = -f (t, y_t)

摘要

The equation y(t) = - f (t, y_t) is considered for t → ∞ The existence of two classes of positive solutions which are asymptotically different is proved using two different techniques _ the method of monotone sequences and the retract method combined with Razumikhin's technique. With the aid of linear estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well. The results are illustrated by an example.