Infinite Systems of Differential Equations II
1979 ◽
Vol 31
(3)
◽
pp. 596-603
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Keyword(s):
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) = [aij(t)] and the nonlinear perturbation were established which guarantee that for each initial value c= {ct} ∈ l1, the system (1.1) has a strongly continuous l1valued 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).
1965 ◽
Vol 5
(2)
◽
pp. 169-195
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1975 ◽
Vol 27
(3)
◽
pp. 691-703
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1976 ◽
Vol 28
(6)
◽
pp. 1132-1145
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1985 ◽
Vol 31
(1)
◽
pp. 127-136
◽
1977 ◽
Vol 34
(3)
◽
pp. 251-264
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1946 ◽
Vol 32
(6)
◽
pp. 190-193
2017 ◽
Vol 55
(2)
◽
pp. 1153-1178
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