On a delay population model with a quadratic nonlinearity without positive steady state

摘要

A population model described by a nonlinear delay differential equation with a quadratic nonlinearityẋ(t)=∑k=1mαk(t)x(hk(t))-β(t)x2(t),t⩾0is considered where m⩾1 is an integer, functions αk,β:[0,∞)→(0,∞) are continuous, functions hk:[0,∞)→R are continuous such that t-τ⩽hk(t)⩽t,τ=const,τ>0, and, for any t⩾0, the inequality hj(t)