TITLE

ON THE TWO-POINT BOUNDARY VALUE PROBLEM FOR QUADRATIC SECOND-ORDER DIFFERENTIAL EQUATIONS AND INCLUSIONS ON MANIFOLDS

AUTHOR(S)
Gliklikh, Yuri E.; Zykov, Peter S.
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The two-point boundary value problem for second-order differential inclusions of the form (D/dt) ṁ(t) ∊ F(t,m(t), ṁ(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.
ACCESSION #
24049407

 

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