Geodesic
Convergence of Solutions of Third Order Differential Equations*
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 779-792

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

Consider a system of differential equations . Solutions of this system are said to be convergent if, given any pair of solutions x(t), y(t), x(t) - y(t) → 0 as t → ∞. In this case the system is also said to be extremely stable.In [6] a technique was developed which yielded the convergence of solutions of the forced Lienard equation. Here a similar technique i s applied to forced third order equations. A critical step in [6] was to show that a certain matrix was negative definite. This could be done directly in [6] since the matrix was only 2 × 2. With third and higher order equations, direct use of necessary and sufficient conditions is not feasible since the computations become unwieldy. 
Swick, K. E. Convergence of Solutions of Third Order Differential Equations*. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 779-792. doi: 10.4153/CMB-1969-101-0
@article{10_4153_CMB_1969_101_0,
     author = {Swick, K. E.},
     title = {Convergence of {Solutions} of {Third} {Order} {Differential} {Equations*}},
     journal = {Canadian mathematical bulletin},
     pages = {779--792},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-101-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-101-0/}
}
TY  - JOUR
AU  - Swick, K. E.
TI  - Convergence of Solutions of Third Order Differential Equations*
JO  - Canadian mathematical bulletin
PY  - 1969
SP  - 779
EP  - 792
VL  - 12
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-101-0/
DO  - 10.4153/CMB-1969-101-0
ID  - 10_4153_CMB_1969_101_0
ER  - 
%0 Journal Article
%A Swick, K. E.
%T Convergence of Solutions of Third Order Differential Equations*
%J Canadian mathematical bulletin
%D 1969
%P 779-792
%V 12
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-101-0/
%R 10.4153/CMB-1969-101-0
%F 10_4153_CMB_1969_101_0

[1] 1. Ezeilo, J. O. C., A note on the convergence of solutions of certain second order differential equations. Port. Math. 24 (1965) 49–58. Google Scholar

[2] 2. Fan, Ky, Inequalities for eigenvalues of Hermitian matrices. U.S. Department of Commerce, National Bureau of Standards, Appl. Math. Ser. 39, 131–139. Google Scholar

[3] 3. La Salle, J. P., A study of synchronous asymptotic stability. Ann. Math. 65 (1957) 571–581. Google Scholar

[4] 4. Lim, Y.S. and Kazda, L. F., A study of second order non-linear systems. J. Math. Anal, and Appl. 8 (1964) 423–444. Google Scholar

[5] 5. Marcus, M. and Mine, H., Introduction to linear algebra. (New York, 1965). Google Scholar

[6] 6. Waltman, P. and Bridgland, T. F. Jr, On convergence of solutions of the forced Iienard equation. J. Math, and Phys. 44 (1965) 284–287. Google Scholar

Cité par Sources :