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AuthorAubin, Jean-Pierre. author
TitleDifferential Inclusions [electronic resource] : Set-Valued Maps and Viability Theory / by Jean-Pierre Aubin, Arrigo Cellina
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1984
Connect tohttp://dx.doi.org/10.1007/978-3-642-69512-4
Descript XIII, 342 p. online resource

CONTENT

0. Background Notes -- 1. Continuous Partitions of Unity -- 2. Absolutely Continuous Functions -- 3. Some Compactness Theorems -- 4. Weak Convergence and Asymptotic Center of Bounded Sequences -- 5. Closed Convex Hulls and the Mean-Value Theorem -- 6. Lower Semicontinuous Convex Functions and Projections of Best Approximation -- 7. A Concise Introduction to Convex Analysis -- 1. Set-Valued Maps -- 1. Set-Valued Maps and Continuity Concepts -- 2. Examples of Set-Valued Maps -- 3. Continuity Properties of Maps with Closed Convex Graph -- 4. Upper Hemicontinuous Maps and the Convergence Theorem -- 5. Hausdorff Topology -- 6. The Selection Problem -- 7. The Minimal Selection -- 8. Chebishev Selection -- 9. The Barycentric Selection -- 10. Selection Theorems for Locally Selectionable Maps -- 11. Michaelโ{128}{153}s Selection Theorem -- 12. The Approximate Selection Theorem and Kakutaniโ{128}{153}s Fixed Point Theorem -- 13. (7-Selectionable Maps -- 14. Measurable Selections -- 2. Existence of Solutions to Differential Inclusions -- 1. Convex Valued Differential Inclusions -- 2. Qualitative Properties of the Set of Trajectories of Convex-Valued Differential Inclusions -- 3. Nonconvex-Valued Differential Inclusions -- 4. Differential Inclusions with Lipschitzean Maps and the Relaxation Theorem -- 5. The Fixed-Point Approach -- 6. The Lower Semicontinuous Case -- 3. Differential Inclusions with Maximal Monotone Maps -- 1. Maximal Monotone Maps -- 2. Existence and Uniqueness of Solutions to Differential Inclusions with Maximal Monotone Maps -- 3. Asymptotic Behavior of Trajectories and the Ergodic Theorem -- 4. Gradient Inclusions -- 5. Application: Gradient Methods for Constrained Minimization Problems -- 4. Viability Theory: The Nonconvex Case -- 1. Bouligandโ{128}{153}s Contingent Cone -- 2. Viable and Monotone Trajectories -- 3. Contingent Derivative of a Set-Valued Map -- 4. The Time Dependent Case -- 5. A Continuous Version of Newtonโ{128}{153}s Method -- 6. A Viability Theorem for Continuous Maps with Nonconvex Images. -- 7. Differential Inclusions with Memory -- 5. Viability Theory and Regulation of Controled Systems: The Convex Case -- 1. Tangent Cones and Normal Cones to Convex Sets -- 2. Viability Implies the Existence of an Equilibrium -- 3. Viability Implies the Existence of Periodic Trajectories -- 4. Regulation of Controled Systems Through Viability -- 5. Walras Equilibria and Dynamical Price Decentralization -- 6. Differential Variational Inequalities -- 7. Rate Equations and Inclusions -- 6. Liapunov Functions -- 1. Upper Contingent Derivative of a Real-Valued Function -- 2. Liapunov Functions and Existence of Equilibria -- 3. Monotone Trajectories of a Differential Inclusion -- 4. Construction of Liapunov Functions -- 5. Stability and Asymptotic Behavior of Trajectories -- Comments


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