Stability of solutions of monotone systems of impulsive differential equations (Q443977)

The impulsive system \[ \begin{aligned} \frac{dx}{dt} &=f(x),\qquad t\neq\tau_k,\\ \Delta x&= g(x(t)), \qquad t=\tau_k \end{aligned} \] is considered, where \(f\in C^1(\mathbb R^n,\mathbb R^n)\), \(x\in \mathbb R^n\), \(f(0)=0\), \(\Delta x=x(t+0)-x(t)\), \(g\in C^1(\mathbb R^n,\mathbb R^n)\), \(g(0)=0\). It is assumed that the vector-function \(f(x)\) is quasimonotone and subadditive. The authors present sufficient conditions for the stability of the zero solution in a cone. Reviewer's remark. (i) In the examples (4.3) and (5.1), the authors do not verify the conditions of the main theorem. (ii) The notation ``Martynuyk-Obolensky criterion'' was first introduced in the paper by \textit{A. Yu. Aleksandrov} and \textit{A. V. Platonov} [Nonlinear Dyn. Syst. Theory 6, No. 1, 17--29 (2006; Zbl 1147.34342)] and is related to the quasimonotonicity of autonomous systems without the assumption of subadditivity of the right-hand side.