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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\mathbb{R}^n,\quad t\in [0,T],\tag{\(*\)} \] subject to the two-point boundary condtion \(y(0)= A\), \(y(T)= B\), where \(A,B\in\mathbb{R}^n\) 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:
34A60 Ordinary differential inclusions
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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