Oscillation and a class of nonlinear differential systems with general deviating arguments

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THE OSCILLATION property ofnonlinear functional differential equations with deviating arguments has drawn a great deal of attention in the last few years. An excellent survey of known results on the subject has been done by Mitropol’skii and Sevelo [l]. Most of the literature, however, has been devoted to the study of scalar differential equations and very little is known about vector (or systems of) differential equations. An effort in the direction of establishing oscillation results for systems of differential equations with deviating arguments was undertaken by Vareh, Gritsai and Sevelo [2] and by the present authors [3]. In this paper we proceed further in this direction to extend the theory developed in [3] to nonlinear differential systems with general deviating arguments of the form

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