Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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We use the Bouligand contingent cone to a subset K of a Hilbert space at x an element of K for defining contingent derivatives of a set-valued map, whose graphs are the contingent cones to the graph of this map, as well as the upper contingent derivatives of a real valued function. We develop a calculus of these concepts and show how they are involved in optimization problems and in solving equations fx0 andor inclusions 0 an element of Fx. They also play a fundamental role for generalizing the Nagumo theorem on flow invariance and for generalizing the concept of Liapunov functions for differential equations andor differential inclusions. Author
- Theoretical Mathematics