On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/30395 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |