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State-Dependent Impulses

Boundary Value Problems on Compact Interval

State-Dependent Impulses by Irena Rachunková
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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.

Atlantis Press; September 2015
194 pages; ISBN 9789462391277
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Title: State-Dependent Impulses
Author: Irena Rachunková; Jan Tomecek
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