Oscillation and linearized oscillation of a logistic equation with several delays

摘要

For a scalar delay logistic equation(*)y′(t)=y(t)∑k=1mrk(t)1−y(hk(t))K,hk(t)⩽t,a connection between oscillating properties of this equation, the corresponding differential inequalities and the linear equationx′(t)+∑k=1mrk(t)x(hk(t))=0is established. Explicit nonoscillation and oscillation conditions are presented. When hk(t)=t−τk,k=1,2,…,m, we also investigate the linearized oscillation of Eq. (*).