ABSTRACT

For high order linear differential equations with deviated arguments, asymptotic behaviour of Kneser type solutions is studied. Using this, quite general assertion (see Lemma 20.6) is proved, which provides a necessary condition for existence of Kneser type solutions. Using this lemma, in case of existence of both linear and nonlinear minorants, a sufficient condition is established for the given equation not to have Kneser type solutions. It is shown that the results obtained for various types of deviations are optimal. For the first order equation, using Schauder-Tychonoff theorem the existence of a Kneser type positive solution is proved.