Abstract
The extension of the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand sides based on the construction of a new version of the method of shifts along trajectories is continued.
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REFERENCES
V. V. Filippov, “On the Aronszajn theorem,” Differentsial'nye Uravneniya [Differential Equations], 33 (1994), no. 1, 75-79.
V. V. Filippov, “On the existence of periodic solutions,” Mat. Zametki [Math. Notes], 61 (1997), no. 5, 769-784.
V. V. Filippov, “On the homological properties of solution sets of ordinary differential equations,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 188 (1997), no. 6, 139-160.
V. V. Filippov, “On the Dirichlet problem for a vector second-order ordinary differential equation,” Differentsial'nye Uravneniya [Differential Equations], 33 (1997), no. 8, 1057-1068.
V. V. Filippov, “The topological structure of spaces of solutions of ordinary differential equations,” Uspekhi Mat. Nauk [Russian Math. Surveys], 48 (1993), no. 1, 103-154.
V. V. Filippov, Spaces of Solutions of Ordinary Differential Equations [in Russian], Moskov. Gos. Univ., Moscow, 1993.
V. V. Filippov, “Basic topological structures of the theory of ordinary differential equations,” in: Topology in Nonlinear Analysis, vol. 35, Banach Center Publications, Warsaw, 1996, pp. 171-192.
V. V. Filippov, Basic Topological Structures of Ordinary Differential Equations, Kluwer Academic Publishers, Dordrecht-Boston-London, 1998.
V. V. Filippov, “A mixture of the Leray-Schauder and Poincare-Andronov methods in the problem about periodic solutions of ordinary differential equations,” Differentsial'nye Uravneniya [Differential Equations], 35 (1999), no. 12, 1709-1711.
V. V. Filippov, “Remarks on periodic solutions of ordinary differential equations,” J. Dynam. Control Systems, 6 (2000), no. 3, 431-451.
R. Engelking, General Topology, PWN, Warsaw, 1983.
V. V. Filippov, “Remarks on guiding functions and periodic solutions,” Differentsial'nye Uravneniya [Differential Equations] (to appear).
J. Mawhin, “Continuation theorems and periodic solutions of ordinary differential equations,” in: Topological Methods in Differential Equations and Inclusions, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995, pp. 291-376.
A. M. Krasnosel'skii, M. A. Krasnosel'skii, and J. Mawhin, “On some conditions for existence of forced periodic oscillations,” Differential Integral Equations, 5 (1992), 1267-1273.
V. V. Filippov, “On the comparison theorem,” Mat. Zametki [Math. Notes], 57 (1995), no. 4, 606-624.
L. Vietoris, “Ñber den höheren Zusammenhang kompakter Räume und eine Klass von zusammen hangstreuen Abbildungen,” Math. Ann., 97 (1927), 454-472.
E. G. Begle, “The Vietoris mapping theorem for bicompact spaces,” Ann. of Math. (2), 51 (1950), no. 3, 534-543.
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Filippov, V.V. On Shifts along Trajectories. Mathematical Notes 74, 266–277 (2003). https://doi.org/10.1023/A:1025064426702
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DOI: https://doi.org/10.1023/A:1025064426702