Geodesic
Stability of Solutions of Ordinary Differential Equations with Respect to a Closed Set
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 720-726

Voir la notice de l'article provenant de la source Cambridge University Press

The stability of the solutions of an ordinary differential equation will be discussed here. The purpose of this note is to compare the stability results which are valid with respect to a compact set and the stability results valid with respect to an unbounded set. The stability of sets is a generalization of stability in the sense of Liapunov and has been discussed by LaSalle (5; 6), LaSalle and Lefschetz (7, p. 58), and Yoshizawa (8; 9; 10). 
Hallam, T. G.; Komkov, V. Stability of Solutions of Ordinary Differential Equations with Respect to a Closed Set. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 720-726. doi: 10.4153/CJM-1968-070-3
@article{10_4153_CJM_1968_070_3,
     author = {Hallam, T. G. and Komkov, V.},
     title = {Stability of {Solutions} of {Ordinary} {Differential} {Equations} with {Respect} to a {Closed} {Set}},
     journal = {Canadian journal of mathematics},
     pages = {720--726},
     year = {1968},
     volume = {20},
     number = {1},
     doi = {10.4153/CJM-1968-070-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-070-3/}
}
TY  - JOUR
AU  - Hallam, T. G.
AU  - Komkov, V.
TI  - Stability of Solutions of Ordinary Differential Equations with Respect to a Closed Set
JO  - Canadian journal of mathematics
PY  - 1968
SP  - 720
EP  - 726
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-070-3/
DO  - 10.4153/CJM-1968-070-3
ID  - 10_4153_CJM_1968_070_3
ER  - 
%0 Journal Article
%A Hallam, T. G.
%A Komkov, V.
%T Stability of Solutions of Ordinary Differential Equations with Respect to a Closed Set
%J Canadian journal of mathematics
%D 1968
%P 720-726
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-070-3/
%R 10.4153/CJM-1968-070-3
%F 10_4153_CJM_1968_070_3

[1] 1. Hahn, W., Theory and applications of Liapunov's direct method (Prentice Hall, Englewood Cliffs, N.J., 1963). Google Scholar

[2] 2. Halanay, A., Differential equations, stability, oscillations, time lags (Academic Press, New York, 1966). Google Scholar

[3] 3. Hallam, T. G., Asymptotic behavior of the solution of an nth order nonhomogeneous ordinary differential equations, Trans. Amer. Math. Soc, 122 (1966), 177–194. Google Scholar

[4] 4. Horowitz, I. M., Synthesis of feedback systems (Academic Press, New York, 1963). Google Scholar

[5] 5. LaSalle, J. P., Recent advances in Liapunov's stability theory, SI AM Rev., 6 (1964), 1–11. Google Scholar

[6] 6. LaSalle, J. P., Some extensions of Liapunov's second method, I.R.E. Trans., Prof. Group on Circuit Theory, 7 (1960), 520–527. Google Scholar

[7] 7. LaSalle, J. P. and Lefschetz, S., Stability by Liapunovfs direct method with applications (Academic Press, New York, 1961). Google Scholar

[8] 8. Yoshizawa, T., Asymptotic behavior of solutions of a system of differential equations, Contributions to Differential Equations, 1 (1963), 371–387. Google Scholar

[9] 9. Yoshizawa, T., Stability of sets and perturbed system, Funkcial. Ekvac, 5 (1962), 31–69. Google Scholar

[10] 10. Yoshizawa, T., Asymptotic behavior of solutions of nonautonomous system near sets, J. Math. Kyoto Univ., 1 (1961/62), 303–323. Google Scholar

Cité par Sources :