Oscillatory and asymptotic properties of differential equations with retarded arguments

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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]).