Listing 1 - 3 of 3 |
Sort by
|
Choose an application
This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years. It comprehensively describes the methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions. Many of the basic techniques and results recently developed about this theory are presented, as well as the literature that is disseminated and scattered in several papers of pioneering researchers who developed the functional analytic framework of this field over the past few decades. Several examples of applications relating to initial and boundary value problems are discussed in detail. The book is intended to advanced graduate researchers and instructors active in research areas with interests in topological properties of fixed point mappings and applications; it also aims to provide students with the necessary understanding of the subject with no deep background material needed. This monograph fills the vacuum in the literature regarding the topological structure of fixed point sets and its applications.
Differential equations. --- Differential inclusions. --- Inclusions, Differential --- Differentiable dynamical systems --- Differential equations --- Set-valued maps --- 517.91 Differential equations --- Differential Equation. --- Differential Inclusion. --- Fixed Point Sets. --- Functional Differential Inclusions. --- Impulsive Differential Equation. --- Impulsive Differential Inclusion. --- Impulsive Semilinear Differential Equation. --- Impulsive Semilinear Differential Inclusion. --- Mild Solution. --- Semigroup. --- Solution Set.
Choose an application
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.
Choose an application
Impulsive differential equations --- Differential inclusions
Listing 1 - 3 of 3 |
Sort by
|