×

zbMATH — the first resource for mathematics

Monotone trajectories of differential inclusions in Banach spaces. (English) Zbl 0877.34018
Let \(E\) be a separable Banach space and \(X\) a nonempty, compact subset of \(E\). Consider the multivalued operator \(F:[0,T]\times X\to P_{cv,wcp}(E)\). The paper contains two existence results for the following problem: Given \(x_0\) in \(X\), we look for Lipschitz solution of the differential inclusion \[ w'(t)\in F(t,w(t)),\quad w(0)=x_0, \] which are viable (i.e. \(w(t)\in X\), for all \(t\in [0,T]\)) and monotone (i.e. for any \(s,t\in [0,t]\), \(s<t\) implies \(w(t)\in P(w(s))\), where \(P(x)= \{y\in X:y\geq x\}\) defines a preorder on \(X\)).

MSC:
34A60 Ordinary differential inclusions
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
PDF BibTeX XML Cite
Full Text: EMIS EuDML