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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Extensions of a theorem of Wintner on systems with asymptotically constant solutions


Author: William F. Trench
Journal: Trans. Amer. Math. Soc. 293 (1986), 477-483
MSC: Primary 34C11; Secondary 34D05
MathSciNet review: 816305
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Abstract: A theorem of Wintner concerning sufficient conditions for a system $ y' = A(t)y$ to have linear asymptotic equilibrium is extended to a system $ x' = A(t)x + f(t,x)$. The integrability conditions imposed on $ f$ permit conditional convergence of some of the improper integrals that occur. The results improve on Wintner's even if $ f = 0$.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0816305-3
Article copyright: © Copyright 1986 American Mathematical Society