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

• Autorzy: Yuri E. Gliklikh , Andrei V. Obukhovski
• Języki publikacji: EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 58C30: Fixed point theorems on manifolds
• 70G45: Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.)
• 58C06: Set valued and function-space valued mappings
• 34A60: Differential inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 41-48

Daty

wydano

2004

otrzymano

2004-04-15

Twórcy

autor

Yuri E. Gliklikh

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

autor

Andrei V. Obukhovski

• 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.

Identyfikatory

DOI

10.7151/dmgt.1051