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State-Dependent Impulses
By writing this book we wanted to present a new approach to impulsive boundary
value problems, which is applicable both to the state-dependent and the fixed-time
impulses. Existence results for boundary value problems with state-dependent
impulses are rather rare in the literature and are given mostly for periodic problems.
Our main goal here is to provide general existence principles which can serve as a
tool for the investigation of solvability of impulsive boundary value problems, in
particular with impulses occurring at moments depending on the state variables. To
demonstrate it, we bring new existence theorems and examples for such problems.
On the other hand, though there is vast literature dealing with fixed-time impulsive
boundary value problems, we decided to include existence results for several
important problems of this type, for example, problems with time or space
singularities.
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