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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Abstract
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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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