Geodesic
Infinite Systems of Differential Equations II
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 596-603

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

This paper is a continuation of earlier work [6], in which we studied the existence and the stability of solutions to the infinite system of nonlinear differential equations (1.1) i = 1, 2, .... Here s is a nonnegative real number, Rs = {t ∈ R: t ≧ s}, and denotes a sequence-valued function. Conditions on the coefficient matrix A(t) = [a ij (t)] and the nonlinear perturbation were established which guarantee that for each initial value c= {c t } ∈ l 1, the system (1.1) has a strongly continuous l 1valued solution x(t) (i.e., each is continuous and converges uniformly on compact subsets of Rs ). A theorem was also given which yields the exponential stability for the nonlinear system (1.1). 
McClure, J. P.; Wong, R. Infinite Systems of Differential Equations II. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 596-603. doi: 10.4153/CJM-1979-060-7
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