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On two point boundary value problems for second order differential inclusions. (English) Zbl 1112.34008

The existence of (almost everywhere) solutions to a second-order differential inclusion

y '' F(t,y,y ' ),y n ,t[0,T],(*)

subject to the two-point boundary condtion y(0)=A, y(T)=B, where A,B n and F is an upper-Carathéodory set-valued map with compact convex values satisfying a quadratic growth condition. The main result relies on some new estimates leading to a priori bounds for solutions to (*) and the usual homotopy continuation method. A discussion of the single-valued counterpart as well as some examples are provided.

MSC:
34A60Differential inclusions
34B15Nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE