On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds | Zendy

Yuri E. Gliklikh | Zendy; Peter S. Zykov | Zendy

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On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds

Author(s) -

Yuri E. Gliklikh,

Peter S. Zykov

Publication year - 2006

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/aaa/2006/30395

Subject(s) - mathematics , quadratic equation , connection (principal bundle) , quadratic differential , differential inclusion , geodesic , covariant transformation , pure mathematics , mathematical analysis , order (exchange) , norm (philosophy) , riemannian manifold , boundary value problem , combinatorics , geometry , law , finance , political science , economics

The two-point boundary value problem for second-order differential inclusions of the form ( D/ dt ) m ˙ ( t )∈F( t,m( t ), m ˙ ( t ) ) on complete Riemannian manifolds is investigated for a couple of points, nonconjugate along at least one geodesic of Levi-Civitá connection, where D/ dt is the covariant derivative of Levi-Civitá connection and F( t,m,X ) is a set-valued vector with quadratic or less than quadratic growth in the third argument. Some interrelations between certain geometric characteristics, the distance between points, and the norm of right-hand side are found that guarantee solvability of the above problem for F with quadratic growth in X . It is shown that this interrelation holds for all inclusions with F having less than quadratic growth in X , and so for them the problem is solvable.