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2004 | 24 | 1 | 41-48
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On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

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Abstrakty
EN
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.
Twórcy
  • Faculty of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394006, Voronezh, Russia
  • Faculty of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394006, Voronezh, Russia
Bibliografia
  • [1] R.L. Bishop and R.J. Crittenden, Geometry of Manifolds, New York, Academic Press 1964, p. 335.
  • [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.
  • [7] M. Kisielewicz, Some remarks on boundary value problem for differential inclusions, Discuss. Math. Differential Inclusions 17 (1997), 43-50.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1051
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