Basic topological structures of the theory of ordinary differential equations

• Autorzy: V. V. Filippov
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 35
• Numer: 1
• Strony: 171-192

Daty

wydano

1996

Twórcy

autor

V. V. Filippov

• Chair of General Topology and Geometry, Department of Mathematics, Moscow State University, 119899, Moscow V-234, Russia

Bibliografia

• [1] R. Bielawski, L. Górniewicz and S. Plaskacz, Topological approach to differential inclusions on closed subsets of $ℝ^n$, Dynamics reported, N1 (new series), Springer-Verlag, 1992, 225-250.
• [2] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw Hill, New York, 1955.
• [3] J. L. Davy, Properties of solution set of generalized differential equation, Bull. Austral. Math. Soc. 6 No3 (1972), 379-398.
• [4] V. V. Fedorchuk and V. V. Filippov, General topology, Basic constructions. Moscow University Publishers, 1988.
• [5] A. F. Filippov, Differential equations with discontinuous right-hand side, Nauka, 1985.
• [6] A. F. Filippov, Differential equations with discontinuous right-hand side, Matem. Sbornik, 51 N1 (1960), 99-128.
• [7] V. V. Filippov, Topological structure of solution spaces of ordinary differential equations, Uspekhi Mat. Nauk 48 N1 (1993), 103-154.
• [8] V. V. Filippov, Solution spaces of ordinary differential equations, Moscow University Publishers, 1993.
• [9] V. V. Filippov, On the existence and properties of solutions of ordinary differential equations and differential inclusions, Doklady AN SSSR, 279 N1 (1984), 47-50.
• [10] V. V. Filippov, Axiomatic theory of solution spaces of ordinary differential equations, Doklady AN SSSR, 280 N2 (1985), 304-308.
• [11] V. V. Filippov, On the theory of solution spaces of ordinary differential equations, Doklady AN SSSR, 285 N5 (1985), 1073-1077.
• [12] V. V. Filippov, On ordinary differential equations with singularities in right-hand side, Mat. zametki 38 N6 (1985), 832-851.
• [13] V. V. Filippov, On the Luzin theorem and right-hand sides of differential inclusions, Mat. zametki 37 N1 (1985), 93-98.
• [14] V. V. Filippov, On the existence and properties of solutions of ordinary differential equations, Differen. Uravnen. 22 N6 (1986), 968-977.
• [15] V. V. Filippov, On the theorem of existence of solutions of ordinary differential equations, Mat. Zametki 40 N6 (1986), 743-748.
• [16] V. V. Filippov, On the theorems of Luzin and Scorza-Dragoni, Vestnik Moskov. Univers. Ser.1, Math.,Mech., N3 (1987), 66-68.
• [17] V. V. Filippov, On the Kneser theorem, Differen. Uravnen. 23 N12 (1987), 2068-2074.
• [18] V. V. Filippov, A note on the Kneser theorem, Vestnik Moskov. Univers. Ser.1, Math. Mech. N1 (1987), 61-63.
• [19] V. V. Filippov, Two notes on the theory of solution spaces of ordinary differential equations, Vestnik Moskov. Univers. Ser.1, Math. Mech. N4 (1988), 53-55.
• [20] V. V. Filippov, The theory of the Cauchy problem for ordinary differential equations from the point of view of general topology, in: General topology. Mappings of topological spaces, Moscow University Publishers, 1988.
• [21] V. V. Filippov, On the asymptotic integration of ordinary differential equations with discontinuity in the right-hand side, Doklady AN SSSR, 321 N3 (1991), 482-485.
• [22] V. V. Filippov, On stationary points and some geometric properties of solutions of ordinary differential equations, Doklady AN SSSR, 323 N6 (1992), 1043-1047.
• [23] V. V. Filippov, On the investigation of ordinary differential equations ``in first approximation'', Differen. Uravnen. 28 N8 (1992), 1351-1355.
• [24] V. V. Filippov, On the asymptotics of solutions of quasilinear ordinary differential equations, Differen. Uravnen. 28 N10 (1992), 1747-1751.
• [25] V. V. Filippov, On the Poincaré-Bendixson theorem and compact families of solution spaces of ordinary differential equations, Mat. Zametki 53 N2 (1993), 140-144.
• [26] V. V. Filippov, On families of changes of variables and the uniqueness theorem for ordinary differential equations, Doklady RAN, 330 N6 (1993), 704-706.
• [27] V. V. Filippov, A note on one theorem of I. T. Kiguradze, Vestnik Moskov. Univers. Ser.1, Math. Mech. N4 (1993), 11-13.
• [28] V. V. Filippov, On the investigation of stationary points in the plane, Vestnik Moskov. Univers. Ser.1, Math. Mech. N5 (1993), 3-10.
• [29] V. V. Filippov, On the theory of the Cauchy problem for an ordinary differential equation with discontinuous right-hand side, Matem. Sbornik N11 (1994), 95-118.
• [30] V. V. Filippov, On sequences of changes of variables and the Lienard equation, Differenc. Uravnen. 30 N3 (1994), 1148-1155.
• [31] V. V. Filippov, On the theorem of uniqueness of the solution of the Cauchy problem for ordinary differential equation, Differen. Uravnen., 30 N6 (1994), 1005-1009.
• [32] V. V. Filippov, On ordinary differential equations with discontinuities in right-hand sides, Differen. Uravnen. 30 N10 (1994).
• [33] Ph. Hartman, Ordinary differential equations, Wiley, 1964.
• [34] B. S. Klebanov, On Ważewski's topological principle, Interim report of the Prague Topological Symposium, 2 (1987), 29.
• [35] B. S. Klebanov, On ω-limit sets of nonautonomous differential equations, Comment. Math. Uni Carolinae 35, N2 (1994), 267-281.
• [36] Cz. Kluczny, Sur certaines familles de courbes en relation avec la théorie des équations différentielles ordinaires, Annales Universitatis M. Curie-Skłodowska, Sec. A., Math. t. XV (1961), 13-40; t. XVI (1962), 5-18.
• [37] H. Kneser, Ueber die Lösungen eines gewöhnlicher Differentialgleichungen das der Lipschitzchen Bedingung nicht genügt, S.-P. Preuss. Akad. Wiss. Phys.-Math. Kl. (1923), 171-174.
• [38] K. Kuratowski, Sur l'espace des fonctions partielles, Ann. di Mat. Pura ed Appl., 40 (1955) 61-67.
• [39] K. Kuratowski, Sur une méthode de métrisation complète, Fund. Math. 43 (1956), 114-138.
• [40] K. Kuratowski, Topology, 1, Academic Press, New York - London, PWN, Warszawa, 1966, 2, 1968.
• [41] P. N. Savel'ev, On the Poincaré-Bendixson theorem and dissipativity in the plane, Vestnik Moskov. Univers. Ser.1, Math. Mech. N3 (1991), 54-55.
• [42] J. Yorke, Spaces of solutions, Mathematical Systems Theory and Economics II, Lecture Notes in Operat. Res. and Math. Econom., Springer-Verlag, 12 (1969), 383-403.
• [43] S. K. Zaremba, Sur certaines familles de courbes en relation avec la théorie des équations différentielles, Rocznik Polskiego Tow. Matemat. t. XV (1936), 83-100.