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

Trench, William F.

doi:10.1090/S0002-9947-1986-0816305-3

Extensions of a theorem of Wintner on systems with asymptotically constant solutions
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by William F. Trench PDF

Trans. Amer. Math. Soc. 293 (1986), 477-483 Request permission

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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