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＜E-Book＞
State-Dependent Impulses : Boundary Value Problems on Compact Interval / by Irena Rachůnková, Jan Tomeček
(Atlantis Briefs in Differential Equations. ISSN:24056413 ; 6)

Edition	1st ed. 2015.
Publisher	(Paris : Atlantis Press : Imprint: Atlantis Press)
Year	2015
Size	XV, 190 p. 7 illus : online resource
Authors	*Rachůnková, Irena author Tomeček, Jan author SpringerLink (Online service)
Subjects	LCSH:Differential equations FREE:Differential Equations
Notes	Introduction -- Second Order Problem with Nonlinear Boundary Conditions -- Dirichlet Problem with Time Singularities -- Dirichlet Problem with Space Singularities -- Systems of Differential Equations and Higher-Order Differential Equations with General Linear Boundary Conditions -- Dirichlet Problem with One Impulse Condition -- Dirichlet Problem via Lower and Upper Functions -- Sturm-Liouville Problem -- Higher Order Equation with General Linear Boundary Conditions -- First Order System with Linear Boundary Conditions 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 HTTP:URL=https://doi.org/10.2991/978-94-6239-127-7

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