Aghezzaf, Brahim; Sajid, Saïd On the second-order contingent set and differential inclusions. (English) Zbl 0958.34010 J. Convex Anal. 7, No. 1, 183-195 (2000). The authors establish the existence of solutions to a nonconvex second-order differential inclusion of the following type: \[ \ddot{x}(t)\in F(x(t), \dot{x}(t)) \text{ a.e, } x(0)=x_0\in K, \dot{x}(0)=v_0\in \Omega, \] such that \(x(t)\in K\), where \(K\) is a closed subset and \(\Omega\) is an open subset of \(\mathbb{R}^n\). When \(K\) is in addition convex, they introduce the contingent cone \(T_K\) to prove the existence of solutions to the differential inclusion: \[ \ddot{x}(t)\in G(x(t),\dot{x}(t)) \text{ a.e, } x(t)\in K \text{ and } \dot{x}(t)\in T_K(x(t)). \] Cited in 1 Document MSC: 34A60 Ordinary differential inclusions 49J24 Optimal control problems with differential inclusions (existence) (MSC2000) 34H05 Control problems involving ordinary differential equations PDFBibTeX XMLCite \textit{B. Aghezzaf} and \textit{S. Sajid}, J. Convex Anal. 7, No. 1, 183--195 (2000; Zbl 0958.34010) Full Text: EuDML EMIS