Geodesic
On Infinite Systems of Linear Differential Equations
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 691-703

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

Let A = [αtj] (i,j = 1, 2, ...) be an infinite matrix with complex entries, and let z = (ζj) (j = 1, 2, ...) be a sequence of complex numbers. In this paper we wish to investigate the existence, uniqueness and asymptotic behavior of solutions to the infinite system of linear differential equations with the initial conditions 
McClure, J. P.; Wong, R. On Infinite Systems of Linear Differential Equations. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 691-703. doi: 10.4153/CJM-1975-077-2
@article{10_4153_CJM_1975_077_2,
     author = {McClure, J. P. and Wong, R.},
     title = {On {Infinite} {Systems} of {Linear} {Differential} {Equations}},
     journal = {Canadian journal of mathematics},
     pages = {691--703},
     year = {1975},
     volume = {27},
     number = {3},
     doi = {10.4153/CJM-1975-077-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-077-2/}
}
TY  - JOUR
AU  - McClure, J. P.
AU  - Wong, R.
TI  - On Infinite Systems of Linear Differential Equations
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 691
EP  - 703
VL  - 27
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-077-2/
DO  - 10.4153/CJM-1975-077-2
ID  - 10_4153_CJM_1975_077_2
ER  - 
%0 Journal Article
%A McClure, J. P.
%A Wong, R.
%T On Infinite Systems of Linear Differential Equations
%J Canadian journal of mathematics
%D 1975
%P 691-703
%V 27
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-077-2/
%R 10.4153/CJM-1975-077-2
%F 10_4153_CJM_1975_077_2

[1] 1. Arley, N. and Borchsenius, V., On the theory of infinite systems of differential equations and their application to the theory of stochastic processes and the perturbation theory of quantum mechanics, Acta Math. 6 (1945), 261–322. Google Scholar

[2] 2. Bellman, R., The boundedness of solutions of infinite systems of linear differential equations, Duke Math. J. H (1947), 695–706. Google Scholar

[3] 3. Hille, E., Pathology of infinite systems of linear first order differential equations with constant coefficients, Ann. Mat. Pura Appl. 55 (1961), 133–148. Google Scholar

[4] 4. Hille, E. and Phillips, R. S., Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., vol. 81 (Amer. Math. Soc, Providence, R.I., 1957). Google Scholar

5. Charles Kahane, Stability of solutions of linear systems with dominant main diagonal, Proc. Amer. Math. Soc. 33 (1972), 69–71. Google Scholar

[6] 6. Krein, S. G., Linear differential equations in Banach space, Translations of Mathematical Monographs, vol. 29 (Amer. Math. Soc, Providence, R.I., 1971). Google Scholar

[7] 7. Lakshmikantham, V. and Leela, S., Differential and integral inequalities, vol. 1 (Academic Press, New York, 1969). Google Scholar

[8] 8. Oguzt, M. N.ôreli, On an infinite system of differential equations occurring in the degradations of polymers, Utilitas Math. 1 (1972), 141–155. Google Scholar

[9] 9. Shaw, Leonard, Existence and approximation of solutions to an infinite set of linear timeinvariant differential equations, SIAM J. Appl. Math. 22 (1972), 266–279. Google Scholar

Cité par Sources :