Abstract
The two-point boundary value problem for second-order
differential inclusions of the form
The two-point boundary value problem for second-order
differential inclusions of the form
L. Bates, “You can't get there from here,” Differential Geometry and its Applications, vol. 8, no. 3, pp. 273–274, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. L. Bishop and R. J. Crittenden, Geometry of Manifolds, vol. 15 of Pure and Applied Mathematics, Academic Press, New York, 1964.
View at: Zentralblatt MATH | MathSciNetYu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, and A. V. Obukhovskiĭ, Introduction to the Theory of Set-Valued Mappings, Voronezh University Press, Voronezh, 1986.
View at: Zentralblatt MATHK. Deimling, Multivalued Differential Equations, vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 1992.
View at: Zentralblatt MATH | MathSciNetB. D. Gel'man and Yu. E. Gliklikh, “Two-point boundary-value problem in geometric mechanics with discontinuous forces,” Prikladnaya Matematika i Mekhanika, vol. 44, no. 3, pp. 565–569, 1980 (Russian).
View at: Google ScholarV. L. Ginzburg, “Accessible points and closed trajectories of mechanical systems,” Appendix F in \cite{10}, pp. 192–201.
View at: Google ScholarYu. E. Gliklikh, “On a certain generalizations of the Hopf-Rinow theorem on geodesics,” Russian Mathematical Surveys, vol. 29, no. 6, pp. 161–162, 1974.
View at: Google ScholarYu. E. Gliklikh, Analysis of Riemannian Manifolds and Problems of Mathematical Physics, Voronezh University Press, Voronezh, 1989.
View at: Zentralblatt MATH | MathSciNetYu. E. Gliklikh, “Velocity hodograph equation in mechanics on Riemannian manifolds,” in Differential Geometry and Its Applications (Brno, 1989), J. Janyška and D. Krupka, Eds., pp. 308–312, World Scientific, New Jersey, 1990.
View at: Google Scholar | Zentralblatt MATHYu. E. Gliklikh, Global Analysis in Mathematical Physics. Geometric and Stochastic Methods, vol. 122 of Applied Mathematical Sciences, Springer, New York, 1997.
View at: Zentralblatt MATH | MathSciNetYu. E. Gliklikh and A. V. Obukhovskiĭ, “A viable solution of a two-point boundary value problem for a second order differential inclusion on a Riemannian manifold,” Proceedings of Voronezh State University, Series Physics, Mathematics, no. 2, pp. 144–149, 2003 (Russian).
View at: Google Scholar | Zentralblatt MATH | MathSciNetYu. E. Gliklikh and A. V. Obukhovskiĭ, “On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds,” Abstract and Applied Analysis, vol. 2003, no. 10, pp. 591–600, 2003.
View at: Google ScholarYu. E. Gliklikh and A. V. Obukhovskiĭ, “On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds,” Discussiones Mathematicae. Differential Inclusions, Control and Optimization, vol. 24, pp. 41–48, 2004.
View at: Google Scholar | MathSciNetD. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Großen, Lecture Notes in Mathematics, no. 55, Springer, Berlin, 1968.
View at: Zentralblatt MATH | MathSciNetM. Kamenskiĭ, V. Obukhovskiĭ, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, vol. 7 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 2001.
View at: Zentralblatt MATH | MathSciNetM. Kisielewicz, “Some remarks on boundary value problem for differential inclusions,” Discussiones Mathematicae. Differential Inclusions, vol. 17, no. 1-2, pp. 43–49, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York, 1963.
View at: Zentralblatt MATH | MathSciNetE. I. Yakovlev, “On solvability of two-end problem for some ordinary second order differential equations on manifolds,” in Baku International Topological Conference. Abstracts. Part 2, p. 361, Baku, 1987.
View at: Google Scholar