Palmucci, Michela; Papalini, Francesca Periodic and boundary value problems for second order differential inclusions. (English) Zbl 1014.34009 J. Appl. Math. Stochastic Anal. 14, No. 2, 161-182 (2001). 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 \(H\). Reviewer: Mouffak Benchohra (Sidi Bel Abbes) Cited in 6 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34A60 Ordinary differential inclusions Keywords:upper solutions; lower solutions; order interval; truncation map; penalty function; tube solution; extremal solutions PDFBibTeX XMLCite \textit{M. Palmucci} and \textit{F. Papalini}, J. Appl. Math. Stochastic Anal. 14, No. 2, 161--182 (2001; Zbl 1014.34009) Full Text: DOI EuDML