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First order dynamic inclusions on time scales. (English) Zbl 1064.34009

The authors deal with the multi-valued boundary value problem

y (t)F(t,y(t))a.e.on[a,b] x ,L(y(a),y(b))=0,(1)

on a time scale 𝕋, where [a,b] x ={t𝕋atb}, F:[a,b] x ×{0} is a multi-valued map with compact and convex values and L: 2 2 is a continuous single-valued map. The proof for the existence of a solution of (1) is based on the method of upper and lower solutions. The authors present some examples to illustrate that if one replaces the -derivative by the Δ-derivative in the dynamic inclusion (1) then such a result holds only under more restrictive assumptions on F.

34A60Differential inclusions
34B15Nonlinear boundary value problems for ODE
34A45Theoretical approximation of solutions of ODE