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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.

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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.

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