Atlantis Briefs in Differential Equations: Boundary Value Problems on Compact Interval

Rachůnková, Irena; Tomeček, Jan

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.

Details

Published by: Atlantis Press

Publication Date: 2015-10-09

Format: Paperback

ISBN-13: 9789462391260

DOI: 10.2991/978-94-6239-127-7

Dimensions: 235cm x155cm

Pages: 190