Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 76, pp. 1-12.
Title: A viability result for second-order differential inclusions
Author: Vasile Lupulescu (Univ. Constantin Brancusi of Targu-Jiu, Romania)
Abstract:
We prove a viability result for the second-order differential inclusion
$$
x''\in F(x,x'),\quad (x(0), x'(0))=(x_0,y_0)\in Q:=K\times \Omega,
$$
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 $V$.
Submitted March 26, 2002. Published August 20, 2002
Math Subject Classifications: 34G20, 47H20.
Key Words: second-order contingent set; subdifferential; viable solution.