Nonautonomous differential equations and topological dynamics. II. Limiting equations
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- by George R. Sell
- Trans. Amer. Math. Soc. 127 (1967), 263-283
- DOI: https://doi.org/10.1090/S0002-9947-1967-0212314-4
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References
- L. Auslander and F. Hahn, Real functions coming from flows on compact spaces and concepts of almost periodicity, Trans. Amer. Math. Soc. 106 (1963), 415–426. MR 144325, DOI 10.1090/S0002-9947-1963-0144325-8
- J. Auslander, N. P. Bhatia, and P. Seibert, Attractors in dynamical systems, Bol. Soc. Mat. Mexicana (2) 9 (1964), 55–66. MR 188535
- E. A. Barbašin, On the theory of general dynamical systems, Učenye Zapiski Moskov. Gos. Univ. 135 (1948), no. Matematika, Tom II, 110–133 (Russian). MR 0033453
- Lawrence G. Deysach and George R. Sell, On the existence of almost periodic motions, Michigan Math. J. 12 (1965), 87–95. MR 173064 W. Hahn, On the general concept of stability and Lyapunov’s direct method, MRC Tech. Rep. 485, Univ. of Wisconsin, Madison, 1964.
- N. N. Krasovskiĭ, Stability of motion. Applications of Lyapunov’s second method to differential systems and equations with delay, Stanford University Press, Stanford, Calif., 1963. Translated by J. L. Brenner. MR 0147744
- J. P. LaSalle, Asymptotic stability criteria, Proc. Sympos. Appl. Math., Vol. XIII, American Mathematical Society, Providence, R.I., 1962, pp. 299–307. MR 0136842
- L. Markus, Asymptotically autonomous differential systems, Contributions to the theory of nonlinear oscillations, vol. 3, Annals of Mathematics Studies, no. 36, Princeton University Press, Princeton, N.J., 1956, pp. 17–29. MR 0081388
- José L. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J. 17 (1950), 457–475. MR 40512
- José L. Massera, Contributions to stability theory, Ann. of Math. (2) 64 (1956), 182–206. MR 79179, DOI 10.2307/1969955
- Richard K. Miller, Asymptotic behavior of solutions of nonlinear differential equations, Trans. Amer. Math. Soc. 115 (1965), 400–416. MR 199502, DOI 10.1090/S0002-9947-1965-0199502-9
- R. K. Miller, Almost periodic differential equations as dynamical systems with applications to the existence of A.P. solutions, J. Differential Equations 1 (1965), 337–345. MR 185221, DOI 10.1016/0022-0396(65)90012-4
- M. I. Minkevič, Theory of integral funnels in dynamical systems without uniqueness, Učenye Zapiski Moskov. Gos. Univ. 135 (1948), no. Matematika, Tom II, 134–151 (Russian). MR 0033454
- V. V. Nemytskii and V. V. Stepanov, Qualitative theory of differential equations, Princeton Mathematical Series, No. 22, Princeton University Press, Princeton, N.J., 1960. MR 0121520
- V. V. Nemyckiĭ, Topological problems of the theory of dynamical systems, Amer. Math. Soc. Translation 1954 (1954), no. 103, 85. MR 0061821
- Z. Opial, Sur la dépendance des solutions d’un systéme d’équations différentielles de leurs seconds membres. Application aux systémes presque autonomes, Ann. Polon. Math. 8 (1960), 75–89 (French). MR 113011, DOI 10.4064/ap-8-1-75-89
- C. R. Putnam, Unilateral stability and almost periodicity, J. Math. Mech. 9 (1960), 915–917. MR 0118899, DOI 10.1512/iumj.1960.9.59055
- George Seifert, Stability conditions for the existence of almost-periodic solutions of almost-periodic systems, J. Math. Anal. Appl. 10 (1965), 409–418. MR 173061, DOI 10.1016/0022-247X(65)90135-6
- George Seifert, Almost periodic solutions for almost periodic systems of ordinary differential equations, J. Differential Equations 2 (1966), 305–319. MR 204775, DOI 10.1016/0022-0396(66)90071-4
- George R. Sell, On the fundamental theory of ordinary differential equations, J. Differential Equations 1 (1965), 370–392. MR 176130, DOI 10.1016/0022-0396(65)90014-8
- George R. Sell, Periodic solutions and asymptotic stability, J. Differential Equations 2 (1966), 143–157. MR 190479, DOI 10.1016/0022-0396(66)90039-8
- George R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc. 127 (1967), 241–262. MR 212313, DOI 10.1090/S0002-9947-1967-0212313-2
Bibliographic Information
- © Copyright 1967 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 127 (1967), 263-283
- MSC: Primary 34.65
- DOI: https://doi.org/10.1090/S0002-9947-1967-0212314-4
- MathSciNet review: 0212314