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Discrete approximations of differential inclusions.
Summary: This paper is devoted to discretization methods for initial value problems for differential inclusions. The main emphasis is on set-valued analogues of Runge-Kutta methods. The material is presented as a survey, simultaneously containing a series of new results. Complete proofs are contained in our extended version [Bayreuther Math. Schr.Lempio, Frank, Veliov, Vladimir
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Covering dimension and differential inclusions.
2000Lower semicontinuous multivalued mappings \(\Phi\), \(\Psi : X \to 2^Y\) are considered, where \(X\), \(Y\) are Banach spaces. Under some assumptions (closedness and convexity of the values of \(\Phi \) and \(\Psi \), surjectivity of \(\Phi \), a certain compactness of \(\Psi\), etc.), it is shown that \[ \dim (\{x \in X;\;\Phi (x) \cap \Psi (x) \neq ...
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