Global attractivity for impulsive population dynamics with delay arguments (Q732575)

Global attractivity results are obtained for the following impulsive delay equation \[ y'(t)+a(t)y(t)+\sum_{i=1}^m p_i(t)f(y(\sigma_i(t))=0, ~t\geq 0,~ t\neq \tau_k, \] \[ y(\tau_k^+)-y(\tau_k) = I_k(y(\tau_k),~ k=1,\dots. \] As a corollary new stability results are obtained for the impulsive logistic delay differential equation. In particular, the non-impulsive autonomous delay logistic equation \[ y'(t)+(1+y(t))\sum_{i=1}^m p_iy(t-\sigma_i) \] is asymptotically stable provided \(\sum_{i=1}^m p_i\sigma_i<1\).