Asymptotics of differential systems with deviating arguments

Trench, William F.

doi:10.1090/S0002-9939-1984-0754707-8

Asymptotics of differential systems with deviating arguments
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by William F. Trench

Proc. Amer. Math. Soc. 92 (1984), 219-224

DOI: https://doi.org/10.1090/S0002-9939-1984-0754707-8

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Abstract:

Conditions are given which imply that a system $X’(t) = F[t,X(g(t))]$ has a solution with some components which approach given limits with specified orders of convergence as $t \to \infty$, while the other components have specified orders of magnitude. The integral smallness conditions on $F$ permit conditional convergence of some of the improper integrals that occur, and it is not required that ${\lim _{t \to \infty }}g(t) = \infty$.

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