Impulsive differential equations and inclusions. (English) Zbl 1130.34003

Contemporary Mathematics and Its Applications, 2. New York, NY: Hindawi Publishing Corporation (ISBN 977-5945-50-X/hbk). xiv, 366 p. (2006).
In this book, the authors present many of their results on impulsive differential equations and inclusions. Many types of problems are considered. In particular, functional and neutral differential inclusions are treated. Also, initial value problems, and periodic and boundary value problems are studied. Mild solutions are obtained when the equations or inclusions contain an infinitesimal generator of a family of suitable operators. Existence results rely on different fixed point theorems for compact, condensing or contractive maps.


34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34A37 Ordinary differential equations with impulses
34A60 Ordinary differential inclusions
34B37 Boundary value problems with impulses for ordinary differential equations
34K45 Functional-differential equations with impulses
35L70 Second-order nonlinear hyperbolic equations
35R12 Impulsive partial differential equations
35R70 PDEs with multivalued right-hand sides