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On systems of boundary value problems for differential inclusions. (English) Zbl 1126.34012
Authors’ abstract: Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34A60 Ordinary differential inclusions
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