Oscillations caused by several retarded and advanced arguments

@article{Ladas1982OscillationsCB,
title={Oscillations caused by several retarded and advanced arguments},
author={G. Ladas and I. Stavroulakis},
journal={Journal of Differential Equations},
year={1982},
volume={44},
pages={134-152}
}

In this paper we study the oscillatory behavior of equations of the forms (*)y′(t) + ∑i = 1nPiy(t − τi) = 0 and (**) y′(t) − ∑i = 1npiy(t + τi) = 0, where piand τi, i = 1, 2,…, n, are positive constants. We prove that each one of the following conditions (1)piτi1/e for some i, i = 1, 2,ߪ, n, (2)(∑i = 1npi)τ>1/e,whereτ = min {τ1,τ2, …, τn}, (3)[Π i = 1nPi]1/n (∑i = 1n τi)>1/e, or (4)(1/n) (∑i = 1n (Piτi)1/2)21/e implies that every solution of (*) and (**) oscillates. A generalization in the case… CONTINUE READING