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Nonlinear boundary value problems for differential inclusions \(y''\in F(t,y,y')\). (English) Zbl 0731.34078

The authors study the system of differential inclusions of the form \(y''\in F(t,y,y')\), \(y\in {\mathcal B}\), where \(F: [a,b]\times {\mathbb{R}}^ n\times {\mathbb{R}}^ n\to {\mathcal K}({\mathbb{R}}^ n)\) is a Carathéodory multifunction, \({\mathcal K}({\mathbb{R}}^ n)\) denotes the family of all nonempty convex and compact subsets of \({\mathbb{R}}^ n\) and \({\mathcal B}\) denotes the (in general, nonlinear) boundary condition. The existence results are proved by means of the topological transversality method of Granas and the a priori bounds technique and may be viewed as improvements of earlier ones, even in the case where F is a single-valued map. At the end the authors apply the obtained results to discuss boundary value problems for differential inclusions on the interval \([0,\infty)\).

MSC:

34K10 Boundary value problems for functional-differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34A60 Ordinary differential inclusions
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