Oscillatory and asymptotic properties of differential equations with retarded arguments

Abstract

We give here some results on oscillatory and asymptotic behavior for differential equations with retarded arguments of arbvitrary order. Lemma 1 establishes a comparison priniple from which we derive the oscillatory anbd asymptotic behavior of the solutions by considering simple ordinary differential equations of the form Y ⁽ⁿ⁾+g(t) Y ^α=0 whose solutions have known behavior. Several known results for diferential equations with retarded arguments and (cf.[1], [6], [8]and[12])are particular cases of ours. Moreover, even in the case of ordinary differential equations, our results appear as generalizations of other ones (cf.[2-4]and[9-11]).