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Boundary value problems. --- Functional differential equations. --- Differential equations, Functional --- Differential equations --- Functional equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Boundary value equations, finite difference equations and systems, nonnegative nonlinearitiesuncoupled multi-point boundary conditions, positive parameters.

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Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Boundary value problems. --- Differential equations. --- Prediction theory. --- Stochastic processes. --- Random processes --- Probabilities --- Forecasting theory --- Stochastic processes --- 517.91 Differential equations --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Boundary Value Problem. --- Condensing. --- Contraction. --- Controllability. --- Differential Inclusion. --- Filippov's Theorem. --- Hyperbolic Differential Inclusion. --- Impulsive Functional Differential Equation. --- Infinite Delay. --- Normal Cone. --- Relaxation. --- Seeping Process. --- Stability. --- Stochastic Differential Equation. --- Variable Times. --- Viable Solution.

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