Periodic boundary value problem for first order differential equations with impulses at variable times
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.
scientific article; zbMATH DE number 1005485