Global linearized stability theory for delay differential equations (Q923916)

The authors investigate the nonlinear delay-differential equation with several time-varying delays \[ x'(t)+ \sum^m_{k=1} f_k(t, x(h_1(t),\dots, x(h_m(t)))= 0, \] where \(h_i(t)\leq t\), \(i= 1,\dots,m\). By suitably bounding of the nonlinear functions \(f_k\) from above and below by linear functions and by assuming a certain asymptotic behavior for the solutions of the corresponding linear equations, the authors obtain asymptotic results for the nonlinear equation. Several examples are discussed.