Stability-like properties of differential inclusions
The author studies some class of properties satisfied by at least one solution of the following Cauchy problem \[ x'(t)\in F\bigl(x(t) \bigr) \quad x(0)= x_0. \tag{1} \] He proved that for some problems, these properties are satisfied by all solutions of \[ x'(t)\in G\bigl(x(t) \bigr) \quad x(0) =x_0 \tag{2} \] where \(G\) is a subset of \(F\) \((\forall x\) \(G(x)\subset F(x))\). In this paper, existence results for such a subinclusion (2) are provided in the framework of many important problems: Invariance, viability, stability, attainability\dots.
scientific article; zbMATH DE number 1045420