Asymptotics of Differential Systems with Deviating Arguments
William F. Trench · Proceedings of the American Mathematical Society · 1984
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 ${\lim _{t \to \infty }}g(t) = \infty$.