Global attractivity in a generalized delay logistic equation (Q1920436)

The main result of the article: Consider the generalized delay logistic equation \[ \dot N(t)= r(t)N(t) \Biggl[1- {{N(g(t))}\over K}\Biggr]^\alpha, \] where \(r\) and \(g\) are continuous functions with \(r(t)>0\), \(g(t)<t\) for \(t\geq 0\) and \(g(t)\to\infty\) as \(t\to\infty\), \(K\) is a positive constant, \(\alpha\geq 1\) is the ratio of two positive odd integers, and \(\int^t_{g(t)} r(s)ds\leq Q\) with \(Q=1\) for \(\alpha\in [1,3]\) and \(Q=\ln 2\) for \(\alpha>3\). Then every oscillatory solution (about \(K\)) converges to \(K\). If, in addition, \(\int_0^\infty r(s)ds=\infty\), then \(K\) globally attracts all positive solutions.