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A stability result for the linear differential equation x”+f(t)x = 0
Published online by Cambridge University Press: 09 April 2009
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Suppose that the real-valued function ƒ(t) is positive, continuous and monotonic increasing for t ≧ t0. If x = x (t) is a solution of the equation for for t ≧ t0, it is known that the solution x(t) oscillates infinitely often as t → ∞ and that the successive maxima of |x(t)| decrease, with increasing t. In particular x(t) is bounded as t → ∞.
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- Copyright © Australian Mathematical Society 1967
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