Geodesic
On the two-point boundary-value problem for equations of geodesics
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 65-70

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For equations of “geodesic spray” type with continuous coefficients on a complete Riemannian manifold, some interrelations between certain geometric characteristics, the distance between points, and the norm of right-hand side are found that guarantee solvability of the boundary-value problem. 
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     title = {On the two-point boundary-value problem for equations of geodesics},
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Yu. E. Gliklikh; P. S. Zykov. On the two-point boundary-value problem for equations of geodesics. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 65-70. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a4/