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

Author

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  • Yuri E. Gliklikh
  • Peter S. Zykov

Abstract

The two-point boundary value problem for second-order differential inclusions of the form ( D / d t ) 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 / d t 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.

Suggested Citation

  • Yuri E. Gliklikh & Peter S. Zykov, 2006. "On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-9, February.
    • Handle: RePEc:hin:jnlaaa:030395
    DOI: 10.1155/AAA/2006/30395
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