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A differential equation in the theory of resonant oscillations of water waves
Published online by Cambridge University Press: 14 November 2011
Synopsis
We show that the problem
has a unique solution and that the asymptotic behaviour of this solution as x → −∞ is given by w(x) = x + B ∣x∣−1/4 cos (b ∣x∣3/2 + φ) + O(x−1), for some constant φ. Here B ≠ 0 depends on ε and In particular there are no even solutions of problem (*) for any ε > 0.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 15 - 26
- Copyright
- Copyright © Royal Society of Edinburgh 1990
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