Electron. J. Diff. Eqns., Vol. 2002(2002), No. 76, pp. 1-12.

A viability result for second-order differential inclusions

Vasile Lupulescu

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.

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Vasile Lupulescu
Universitatea ``Constantin Brancusi'' of Targu-Jiu
Bulevardul Republicii, Nr.1
1400 T\^{a}rgu-Jiu, Romania
e-mail: vasile@utgjiu.ro

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