More on linearized stability for neutral equations with state-dependent delays
The author proves the principle of linearized stability for semiflows generated by neutral functional differential equations. The state space is a closed subset in a manifold of \(C^2\)-functions. Applications include equations with state-dependent delay, as for example \[ x'(t) = A(x'(t+d(x(t))))+f(x(t+r(x(t)))) \] with nonlinear functions \(A\: \mathbb R\to \mathbb R\) and \(d\: \mathbb R\to (-h,0)\), \(f\: \mathbb R\to \mathbb R\), \(r\: \mathbb R\to[-h,0]\).
scientific article; zbMATH DE number 6111588