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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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On differential inclusions with an advanced argument
1992A differential inclusion with an advanced argument, \[ x'(t)\in F(t,x(t),x(\nu(t))),\tag{1} \] is considered in a separable, reflexive Banach space \(X\). It is assumed that \(\nu(t)\geq t\). The set-valued map \(F\) has non- empty compact convex values and it is \({\mathcal L}\times {\mathcal B}(X\times X)\)-measurable and upper semicontinuous on \(X ...
Kaczor, Wiesława (1949- ) +1 more
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H∞ observer design for singular one-sided Lur'e differential inclusion system
Journal of the Franklin Institute, 2017Jun Huang +4 more
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Managing urban diversity through differential inclusion in Singapore
, 2017Junjia Ye
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Managing illegality at the internal border: Governing through ‘differential inclusion’ in Italy
, 2017G. Fabini
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Multiple solutions for a Robin‐type differential inclusion problem involving the p(x)‐Laplacian
, 2017B. Ge, Qing-Mei Zhou
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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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