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|Title:||Asymptotic behaviour of the solution of a functional-differential equation|
|Citation:||Maths Technical Papers (Brunel University). January 1984, pp 1-15|
|Abstract:||The asymptotic behaviour as t→∞ of the solution of the functional- differential equation y'(t) = -y(t/k), with y(0) = 1 and k > 1 , is derived from an integral representation by the method of steepest descents. It is shown that the solution oscillates (that is, has arbitrarily large zeros), that the amplitude of the oscillations growsfasterthan any polynomialbut slower thananyexponential, and that the ratios of successive zeros of the solution decrease to the limiting value k.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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