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Abstract: : We consider the linear differential equation "y 00 + '(x; ")y 0 + /(x; ")y = 0 where " ? 0 is a small parameter and where x'(x; 0) ? 0 if x 6= 0. We suppose that ' and / are real analytic on [a; b ] \Theta f0g and that the function / 0 : x 7! /(x; 0) has a zero at x = 0 of at least the same order as ' 0 : x 7! '(x; 0). We call resonant solution a (family of) solution y " : [a; b] ! IR tending uniformly to a non trivial solution of the reduced equation '(x; 0)y 0 +/(x; 0)y = 0 obtained... (Update)
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BibTeX entry: (Update)
@misc{ fruchard-overstability,
author = "Augustin Fruchard and Reinhard Schäfke",
title = "Overstability and Resonance",
url = "citeseer.ist.psu.edu/fruchard00overstability.html" }
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