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On two-point boundary value problems for second-order differential inclusions on manifolds

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We investigate the two-point boundary value problem for second-order differential inclusions of the form  [image omitted] on a complete Riemannian manifold for a couple of points, non-conjugate along at least one geodesic of Levi-Civita connection, where  [image omitted] is the covariant derivative of Levi-Civita connection and F(t, m, X) is a set-valued vector field (it is either convexvalued and satisfies the upper Caratheodory condition or it is almost lower semi-continuous) such that  [image omitted] where f : [0, ∞) → [0, ∞) is an arbitrary continuous function, increasing on [0, ∞). Some conditions on certain geometric characteristics, on the distance between points and on the length of time interval, under which the problem is solvable, are found. A generalization to inclusions of the same sort subjected to a non-holonomic constraint is also presented.

Keywords: Riemannian manifolds; constraint; non-conjugate points; second-order differential inclusions; two-point boundary value problem

Document Type: Research Article


Affiliations: Physics and Mathematics Faculty, Kursk State University, 305416 Kursk, Russia

Publication date: June 1, 2009

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