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Periodic and boundary value problems for second order differential inclusions. (English) Zbl 1014.34009

Here, the authors investigate the existence of extremal solutions to the multivalued boundary value problem \[ -x''(t)\in F(t,x(t),x'(t)) \;\text{a.e.} \;t\in T=[0,b], \] subjected to nonhomogeneous Sturm-Liouville boundary conditions and Dirichlet conditions at the points \(t=0\) and \(t=b\). By means of the concept of upper and lower solutions combined with the Kakutanu-Ky Fan theorem, the authors consider the cases when the multivalued map \(F\) takes values in \(\mathbb{R}\) and in a Hilbert space \(H\).

MSC:

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