On the differential inclusion \(x^\prime\in[-1, +1]\). (English) Zbl 0922.34009

Cellina, Arrigo

Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 69, 1-6 (1980).

It is proved that the set \(K_0\) of solutions to the equation \(x'\in(-1,+1)\), \(x(0)=0\), is a subset of first category of the set \(K\) of solutions \(x'\in[-1,+1]\).

MSC:

34A60	Ordinary differential inclusions
49J50	Fréchet and Gateaux differentiability in optimization