Linearized oscillation theory for a nonlinear nonautonomous delay differential equation

摘要

Oscillation properties of two following equations are compared: a scalar nonlinear delay differential equationẏ(t)+∑k=1mrk(t)fk[y(hk(t))]=0with rk(t)⩾0,hk(t)⩽t, and a linear delay differential equationẋ(t)+∑k=1mrk(t)x(hk(t))=0.Coefficients rk(t) and delays are not assumed to be continuous. As an application, explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics.