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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 $$y''\in F(t, y,y'),\quad y\in\bbfR^n,\quad t\in [0,T],\tag{$*$}$$ subject to the two-point boundary condtion $y(0)= A$, $y(T)= B$, where $A,B\in\bbfR^n$ 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.

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