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State-Dependent Impulses : Boundary Value Problems on Compact Interval / by Irena Rachůnková, Jan Tomeček.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Rachůnková, Irena., Author.
- Tomeček, Jan., Author.
- Series:
- Atlantis Briefs in Differential Equations, 2405-6413 ; 6
- Language:
- English
- Subjects (All):
- Differential equations.
- Differential Equations.
- Local Subjects:
- Differential Equations.
- Physical Description:
- 1 online resource (194 p.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- 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.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references and index.
- ISBN:
- 94-6239-127-0
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