Abstract
Hill's equation is a real linear second-order ordinary differential equation with a periodic coefficient f(t): y(t)+[λ+ e f (t)] y(t) = 0. (0.1) It has unbounded solutions for certain intervals of the real parameter A, called instability intervals. Here these intervals, and the growth rate of the unbounded solutions, are determined for e small, and also for A large. This is done by constructing a fundamental pair of solutions which are power series in e/A 1/2 , with coefficients that are bounded functions of A.
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