Note on continuity of dependence of solutions of differential inclusion \(y'\in F(t,y)\) on the right hand side (Q1358547)

This article makes a comment to a series of the author's investigations [see for example \textit{V. V. Filippov}, Differ. Equations 23, No. 12, 1391-1395 (1987); translation from Differ. Uravn. 23, No. 12, 2068-2074 (1987; Zbl 0679.34003), Sov. Math., Dokl. 30, 616-619 (1984); translation from Dokl. Akad. Nauk SSSR 279, 47-50 (1984; Zbl 0593.34012), Differ. Equations 22, 681-688 (1986); translation from Differ. Uravn. 22, No. 6, 968-977 (1986; Zbl 0612.34014)]. The main result is on the continuous (strictly speaking, the upper semicontinuous) dependence of the inclusion's \[ y' \in F(t,y,\alpha) \] solutions (and equation's \(y' = F(t,y,\alpha)\) solutions) on the parameter \(\alpha\). Three examples are given where the continuous dependence of the solutions on the parameter \(\alpha\) follows for \(\alpha \not= 0\) from classical theorems whereas for \(\alpha = 0\) continuity follows from the author's theorems.