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Second order boundary value problems of discontinuous differential inclusions. (English) Zbl 1088.34505

The authors prove existence results for the following boundary value problem for second-order differential inclusions \[ -x''(t)\in F(t,x(t)) \,\,\, \text{a.e.}\,\,\, t\in J:=[t_0,t_1], \quad x(t_0)=0=x(t_1), \] where \(F: J\times {\mathbb R}\to {\mathcal P}(\mathbb R)\) (\({\mathcal P}(\mathbb R)\) is the class of all nonempty subsets of \({\mathbb R}\)), under some monotonicity condition and without the continuity of the multi-valued function.

MSC:

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