Differential Inclusions, Control and Optimization 24 (2004) 41-48
doi: 10.7151/dmdico.1051

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ON DIFFERENTIAL INCLUSIONS OF VELOCITY HODOGRAPH TYPE WITH CARATHÉODORY CONDITIONS ON RIEMANNIAN MANIFOLDS

Yuri E. Gliklikh and Andrei V. Obukhovski

Faculty of Mathematics
Voronezh State University
Universitetskaya pl., 1
394006, Voronezh, Russia

e-mail: yeg@alg.vsu.ru
e-mail: avo@mathd.vsu.ru

Abstract

We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.

Keywords: differential inclusions, Carathéodory conditions, velocity hodograph, Riemannian manifold, two-point bounadry value problem.

2000 Mathematics Subject Classification: 58C06, 58C30, 34A60, 70G45.

References

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Received 15 April 2004