# On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

Yuri E. Gliklikh; Andrei V. Obukhovski

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2004)

- Volume: 24, Issue: 1, page 41-48
- ISSN: 1509-9407

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topYuri E. Gliklikh, and Andrei V. Obukhovski. "On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 24.1 (2004): 41-48. <http://eudml.org/doc/271514>.

@article{YuriE2004,

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.},

author = {Yuri E. Gliklikh, Andrei V. Obukhovski},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {differential inclusions; Carathéodory conditions; velocity hodograph; Riemannian manifold; two-point bounadry value problem; Carathéodory condition; two-point boundary value problem},

language = {eng},

number = {1},

pages = {41-48},

title = {On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds},

url = {http://eudml.org/doc/271514},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Yuri E. Gliklikh

AU - Andrei V. Obukhovski

TI - On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2004

VL - 24

IS - 1

SP - 41

EP - 48

AB - 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.

LA - eng

KW - differential inclusions; Carathéodory conditions; velocity hodograph; Riemannian manifold; two-point bounadry value problem; Carathéodory condition; two-point boundary value problem

UR - http://eudml.org/doc/271514

ER -

## References

top- [1] R.L. Bishop and R.J. Crittenden, Geometry of Manifolds, New York, Academic Press 1964, p. 335. Zbl0132.16003
- [2] Yu.G. Borisovich, B.D. Gel'man, A.D. Myshkis and V.V. Obukhovski, Introduction to the theory of multivalued maps, Voronezh, Voronezh University Press, 1986, p. 104 (Russian).
- [3] B.D. Gel'man and Yu.E. Gliklikh, Two-point boundary-value problem in geometric mechanics with discontinuous forces, Prikladnaya Matematika i Mekhanika 44 (3) (1980), 565-569 (Russian).
- [4] Yu.E. Gliklikh, On a certain generalization of the Hopf-Rinow theorem on geodesics, Russian Math. Surveys 29 (6) (1974), 161-162.
- [5] Yu.E. Gliklikh, Global Analysis in Mathematical Physics, Geometric and Stochastic Methods, New York, Springer-Verlag 1997, p. xv+213.
- [6] M. Kamenski, V. Obukhovski and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, Berlin-New York, Walter de Gruyter 2001, p. 231. Zbl0921.34017
- [7] M. Kisielewicz, Some remarks on boundary value problem for differential inclusions, Discuss. Math. Differential Inclusions 17 (1997), 43-50.

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