Impulsive Differential Equations and Inclusions

In the last several years, impulsive differential and functional differential equations and inclusions have assumed an increasing relevance, mainly due to the great variety of problems arising in sciences, engineering and technology which can be described by such types of equations and inclusions. This book is devoted to this rapidly developing theory of differential equations and inclusions with special emphasis on such equations and inclusions subject to impulses. In addition, the book includes a wide account of various applications to physical problems.

The book consists of twelve chapters. Initial value problems and boundary value problems for both impulsive differential equations and differential inclusions, as well as for both impulsive functional differential equations and functional differential inclusions, or for both neutral functional differential equations and neutral functional differential inclusions, are studied. Moreover results on impulsive semilinear ordinary differential inclusions and functional differential inclusions satisfying nonlocal boundary conditions are given extensive attention. Positive solutions and multiple positive solutions for impulsive ordinary differential equations and functional differential equations, as well as impulsive differential inclusions satisfying periodic boundary conditions are also studied.

Some of these results are extended to functional differential equations and functional differential inclusions with variable times, to semilinear functional differential equations and functional differential inclusions for operators that are nondensely defined on a Banach space, to impulsive hyperbolic differential inclusions, and to impulsive dynamic equations on time scales.

Each chapter concludes with a section devoted to notes and bibliographical remarks. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists and physicists.