Periodic boundary value problem for first order differential equations with impulses at variable times (Q1353478)

The authors study the periodic boundary value problem with impulses at variable times given by the system of equations \[ \begin{aligned} u'(t) &= f(t,u(t)), \qquad t\in J,\quad t\neq\gamma(u(t)),\\ u(t^+)&= u(t)+ I(u(t)), \quad t=\gamma(u(t)) \;\text{ and } u(0)= u(T),\end{aligned} \] where \(J=[0,T]\), \(f\in C(J\times \mathbb{R},\mathbb{R})\), \(I\in C'(\mathbb{R},\mathbb{R}^-)\) and \(\gamma\in C'(\mathbb{R},\mathbb{R})\). As the main result they show that the method of upper and lower solutions is applicable to this system.