Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand sides (differential inclusions). An explicit description of corresponding topological structures expands the theory in the case of equations with continuous right hand sides also. In reality, this is a new science where Ordinary Differential Equations, General Topology, Integration theory and Functional Analysis meet. In what concerns equations with discontinuities and differential inclu sions, we do not restrict the consideration to the Cauchy problem, but we show how to develop an advanced theory whose volume is commensurable with the volume of the existing theory of Ordinary Differential Equations. The level of the account rises in the book step by step from second year student to working scientist.

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.

In this book we present a significant part ofthe material given in an autumn school on "Nonlinear Analysis and Differential Equations," held at the CMAF (Centro de Matematica e Aplica