Nonmonotone Lyapunov functionals in uniform asymptotic stability analysis of delay equations (Q1873457)

The equation \[ \dot x(t)=f(t,x_t), \,\,f(t,0)\equiv 0, \] is considered, where \(t\in \mathbb R_+\), \(f(t,\,\cdot\,): C([-r(t),0],\mathbb R^n)\to \mathbb R^n\), \(x_t=x(t+\theta)\), \(\theta\in [-r(t),0]\) and \(r'(t)<\Delta<1\). The uniform asymptotic stability of the trivial solution is studied with the aid of suitable Lyapunov functionals.