State-Dependent Impulses - Irena Rachunková Jan Tomecek Kartoniert (TB)

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems including a new approach giving effective conditions for the solvability of the Dirichle t problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm-Liouville boundary value problem for a more general right-hand side of a differential equation. Finally we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.