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Existence theorems for a multivalued boundary value problem. (English) Zbl 0741.34008
The multivalued boundary value problem \(u''\in F(t,u,u')\), \(u(a)=u(b)=0\), is considered where \(F\) has closed convex values in \(R^ n\), the graphs of \(F(t,\centerdot,\centerdot)\) are closed, the maps \(F(\centerdot,u,u')\) are measurable and \(F\) is bounded in some sense. The existence of solutions \(u\in W^{2,p}([a,b],R^ n)\) is proved using a recent existence result for operator inclusions.

34B15 Nonlinear boundary value problems for ordinary differential equations
34A60 Ordinary differential inclusions
47J25 Iterative procedures involving nonlinear operators
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI
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