A viability result for second-order differential inclusions.
Vasile Lupulescu · DOAJ (DOAJ: Directory of Open Access Journals) · 2002
We prove a viability result for the second-order differential inclusion $$ x''in F(x,x'),quad (x(0), x'(0))=(x_0,y_0)in Q:=Kimes Omega, $$ where $K$ is a closed and $Omega$ is an open subsets of $mathbb{R}^m$, and is an upper semicontinuous set-valued map with compact values, such that $F(x,y) subset partial V(y)$, for some convex proper lower semicontinuous function $V$.