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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