Weak tangency, weak invariance, and Carathéodory mappings
The authors obtain new results on weak invariance in Hilbert spaces both in autonomous and nonautonomous case. First, they consider a multifunction from a Hilbert space \(H\) to nonempty subsets of \(H\) which is upper hemicontinuous and satisfies a growth condition and they give necessary and sufficient conditions for a subset \(S\) of \(H\) to be approximately weakly invariant with respect to approximate solutions to the differential inclusion \(\dot{x}(t) \in F(x(t))\). Then, they consider also the nonautonomous case in which the multifunction is defined on \([a,b) \times H\) into \(H\) and they extend the previous result to the case where the multifunction is of Carathéodory type. In the final part, some applications are presented.
scientific article; zbMATH DE number 1845285