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Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side. (English) Zbl 0935.34009
The paper concerns the existence of solutions to the multivalued problem $u''(t)\in F(t,u(t),u'(t)), \quad u(a)=u(b)=0.$ Here, $$F:[a,b]\times \mathbb{R}^n\times \mathbb{R}^n\to \mathbb{R}^n$$ is a multifunction with possibly nonconvex and unbounded values. The main result states that there exists a suitable multifunction $$G:[a,b]\times \mathbb{R}^n\times \mathbb{R}^n\to \mathbb{R}^n$$ with convex and bounded values such that every solution to the corresponding multivalued problem is a solution to the former one. Applications are given to the existence of solutions to implicit boundary value problems.
Reviewer: C.Ursescu (Iaşi)

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34A60 Ordinary differential inclusions 34A09 Implicit ordinary differential equations, differential-algebraic equations
##### Keywords:
solutions; multivalued boundary value problem; existence
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