State-Dependent Impulses: Boundary Value Problems on Compact Interval (Atlantis Briefs in Differential Equations
Irena Rachůnková, "State-Dependent Impulses: Boundary Value Problems on Compact Interval (Atlantis Briefs in Differential Equations "
English | ISBN: 9462391262 | 2015 | 205 pages | EPUB | 4 MB
English | ISBN: 9462391262 | 2015 | 205 pages | EPUB | 4 MB
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 Dirichlet 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.