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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.
List of contents
Nonsmooth critical point theory and quasilinear elliptic equations.- Théorèmes d'existence de solutions d'inclusions différentielles.- Second order differential equations on manifolds and forced oscillations.- Topological approach to differential inclusions.- Effects of delays on dynamics.- Existence principles for differential equations and systems of equations.- Continuation theorems and periodic solutions of ordinary differential equations.- Some applications of the topological degree to stability theory.- The center manifold technique and complex dynamics of parabolic equations.- Positive solutions of semilinear elliptic boundary value problems.- Cinq cours sur les équations différentielles dans les espaces de Banach.
