Instability criteria are obtained for systems described byẋ = A(t)xwhen the parameters are slowly varying. In particular it is shown that, whenA(t)has eigenvalues in the right-half plane and all eigenvalues are bounded away from the imaginary axis, then ift ≥ 0 ∥ Ȧ(t) sufficiently small, the system has unbounded solutions. Results are also given for systems of the formẋ = A(t)x + f(x, t), and the dichotomy of solutions is studied in both the linear and nonlinear cases.
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Ronald A. Skoog (1972) studied this question.
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