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Paperback, 289 pages, NOT ex-library. A faint beige stain on lower outer page edges externally, also showing - very vaguely - in lower corner of the last and first page inside the book. Else clean and bright with limited wear, firm binding, unmarked text. Free of inscriptions and stamps. -- A collection of advanced research and expository articles in the fields of differential inclusions, topological fixed-point theory, and optimal control. Originating from a 1997 mini-semester hosted by the International Stefan Banach Mathematical Center in Warsaw, in cooperation with the Juliusz Schauder Center for Nonlinear Studies, the volume gathers contributions from leading international mathematicians and emerging scholars, making it a valuable reference point for both established researchers and early-career mathematicians in nonlinear analysis. The book is divided into three thematic sections: differential inclusions, topological methods, and optimal control theory. The topics converge around the role of set-valued and multivalued mappings in modern mathematical systems, exploring how topological and variational methods can be applied to increasingly complex differential problems. The first section deals with the existence, uniqueness, periodicity, and stability of solutions to quasi-linear and semilinear differential inclusions, including works on discontinuous systems (Bressan and Shen), nonlocal boundary value problems (Allegretto and Nistri), and multivalued Nielsen fixed-point theory (Andres, Gorniewicz, and Juzierski). These contributions deepen the theoretical framework for dynamic systems influenced by non-deterministic or discontinuous dynamics. The second section focuses on topological tools and fixed-point theorems, including generalizations of the Borsuk-Ulam theorem (Dzedzej and Izydorek), graph approximations of set-valued maps (Kryszewski), and Leray-Schauder-type theorems with applications to equilibria (Idzik and Park). These provide robust techniques for handling abstract inclusions that arise in infinite-dimensional or nonconvex settings. The third section applies these tools to optimal control problems, Hamilton-Jacobi-Bellman equations, and differential games. Several papers address the uniqueness and regularity of optimal trajectories, shock formation, and state constraints in optimal control theory (Byrnes and Frankowska; Frankowska and Plaskacz). Other contributions explore convex and variational methods, including approximate solutions in the calculus of variations (Moussaoui and Seeger) and conditions for equilibrium in constrained systems. This volume will be especially relevant for researchers interested in the rigorous treatment of dynamical systems governed by multivalued maps, offering a combination of foundational theory, advanced techniques, and applications to physics, mechanics, and control theory.
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