Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Nonautonomous differential equations and topological dynamics. II. Limiting equations


Author: George R. Sell
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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] 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 0144325 (26:1871)
  • [2] J. Auslander, N. P. Bhatia and P. Seibert, Attractors in dynamical systems, Bol. Soc. Mat. Mexicana (1964), 55-66. MR 0188535 (32:5973)
  • [3] E. A. Barbašin, On the theory of general dynamical systems, Učen. Zap. Moskov. Gos. Univ. 135 Matematika 2 (1948), 110-133. (Russian) MR 0033453 (11:443c)
  • [4] L. G. Deysach and G. R. Sell, On the existence of almost periodic motions, Michigan Math. J. 12 (1965), 87-95. MR 0173064 (30:3279)
  • [5] W. Hahn, On the general concept of stability and Lyapunov's direct method, MRC Tech. Rep. 485, Univ. of Wisconsin, Madison, 1964.
  • [6] N. N. Krasovskii, Stability of motion, Stanford Univ. Press, Palo Alto, Calif., 1963. MR 0147744 (26:5258)
  • [7] J. P. LaSalle, Asymptotic stability criteria, Proc. Sympos. Appl. Math. Vol. 13, pp. 299-307, Amer. Math. Soc., Providence, R. I., 1962. MR 0136842 (25:303)
  • [8] L. Markus, Asymptotically autonomous differential systems, Contributions to Nonlinear Oscillations, Vol. 3, Princeton Univ. Press, Princeton, N. J., 1956. MR 0081388 (18:394a)
  • [9] J. L. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J. 17 (1950), 457-475. MR 0040512 (12:705g)
  • [10] -, Contributions to stability theory, Ann. of Math. (2) 64 (1956), 182-206. MR 0079179 (18:42d)
  • [11] R. K. Miller, Asymptotic behavior of solutions of nonlinear differential equations, Trans. Amer. Math. Soc. 115 (1965), 400-416. MR 0199502 (33:7646)
  • [12] -, Almost periodic differential equations as dynamical systems with applications to the existence of a.p. solutions, J. Differential Equations 1 (1965), 337-345. MR 0185221 (32:2690)
  • [13] M. I. Minkevič, Theory of integral funnels in dynamical systems, Učen. Zap. Moskov. Gos. Univ. 135 Matematika 2 (1948), 134-151. (Russian) MR 0033454 (11:443d)
  • [14] V. V. Nemyckiĭ and V. V. Stepanov, Qualitative theory of differential equations, Princeton Univ. Press, Princeton, N. J., 1960. MR 0121520 (22:12258)
  • [15] V. V. Nemyckiĭ, Topological problems of the theory of dynamical systems, Uspehi Mat. Nauk 4 (1949), 91-153; English transl., Amer. Math. Soc. Transl. (1) 5 (1962), 414-497. MR 0061821 (15:889f)
  • [16] Z. Opial, Sur la dépendance des solutions d'un système d'équations différentielles de leurs seconds membres. Applications aux systèmes presque autonomous, Ann. Polon. Math. 8 (1960), 75-89. MR 0113011 (22:3852)
  • [17] C. R. Putnam, Unilateral stability and almost periodicity, J. Math. Mech. 9 (1960), 915-917. MR 0118899 (22:9668)
  • [18] G. Seifert, Stability conditions for the existence of almost-periodic solutions of almost-periodic systems, J. Math. Anal. Appl. 10 (1965), 409-418. MR 0173061 (30:3276)
  • [19] -, Almost periodic solutions for almost periodic systems of ordinary differential equations, J. Differential Equations 2 (1966), 305-319. MR 0204775 (34:4613)
  • [20] G. R. Sell, On the fundamental theory of ordinary differential equations, J. Differential Equations 1 (1965), 370-392. MR 0176130 (31:405)
  • [21] -, Periodic solutions and asymptotic stability, J. Differential Equations 2 (1966), 143-157. MR 0190479 (32:7891)
  • [22] -, Nonautonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc. 127 (1967), 241-262. MR 0212313 (35:3187a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34.65

Retrieve articles in all journals with MSC: 34.65


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1967-0212314-4
Article copyright: © Copyright 1967 American Mathematical Society

American Mathematical Society