Almost periodic solutions of nonlinear delay population equation with feedback control (Q864203)

For the system \[ x'(t)= x(t)\biggl(r(t)- a(t) x(t)- \sum^n_1 b_j(t) x^{\beta_j}(t- \sigma_j)- c(t) u(t)\biggr), \] \[ u'(t)=- \eta(t) u(t)+ \sum^n_{j=1} g_j(t) x^{\beta_j}(t- \sigma_j) \] with positive real \(\alpha\), \(\beta_j\) and positive Bohr almost periodic \(r\), \(a\), \(c\), \(\eta\), \(b_j\), \(g_j\) the existence of a positive uniformly asymptotically stable Bohr almost periodic solution \(x\), \(u\) on \(\mathbb{R}\) is stated, provided \(\text{inf}_r\) is sufficiently large and another inequality between the \(a,\dots, g_j\) holds. (There is no proof for the existence of a (bounded) solution on \((-\infty, t_0]\)).