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Oscillation and nonoscillation in delay or advanced differential equations and in integrodifferential equations. (English) Zbl 0930.34050
New sufficient conditions are obtained for the oscillation of all solutions to a class of linear homogeneous first-order delay/advanced differential equations with variable coefficients and variable delays or advanced arguments. The existence of positive solutions is discussed for such delay/advanced equations under certain conditions. Necessary conditions are derived on certain homogeneous linear first-order integrodifferential equations to have positive solutions. Sufficient conditions are given for the existence of positive solutions which tend to zero as t for such integrodifferential equations.
MSC:
34K11Oscillation theory of functional-differential equations
45J05Integro-ordinary differential equations