ASYMPTOTICS OF RAPIDLY VARYING SOLUTIONS OF DIFFERENTIAL EQUATIONS ASYMPTOTICALLY CLOSE TO EQUATIONS WITH REGULARLY VARYING NONLINEARITIES

摘要

We establish the existence conditions and asymptotic representations as t ↑ ω (ω ≤ + ∞) for rapidly varying solutions of differential equations of order n asymptotically close (in a certain sense) to equations with regularly varying nonlinearities.