OSCILLATIONS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS GENERATED BY RETARDED ACTIONS

Abstract

This chapter discusses the oscillations of nonlinear functional differential equations generated by retarded actions. It presents an investigation of the oscillatory and asymptotic behavior of solutions of nonlinear second order functional differential equations. In doing so, all solutions of such equations are classified in regard to their behavior as t → ∞ and to their oscillatory nature. The results generalize the results for nonlinear second order functional differential equations. The oscillation results to nonlinear second order functional differential equations are extended under certain growth conditions on an equation and on delay. This oscillatory behavior is generated by retarded actions and vanishes when retarded action vanishes. The sufficient growth conditions on fi (t, u, v) and functional arguments under which the set S0USeS-e defined is empty and consequently every bounded solution is oscillatory. Clearly, these oscillations are caused by the retarded actions and vanish if delay vanishes.