Oscillations in integrodifferential equations of arbitrary order (Q1095335)

The author gives sufficient conditions for all bounded solutions of a class of scalar linear integrodifferential equations of nth order on \((0,+\infty)\) (n a positive integer) to be either oscillatory or converge to zero, as \(t\to \infty\). In the case of linear delay-differential equations, the sufficient conditions are also shown to be necessary for all bounded solutions to be oscillatory. By means of a comparison with an appropriate linear equation, similar results are derived for nonlinear integrodifferential and delay-differential equations.