Resonance Tongues in Hill's Equations: A Geometric Approach
✍ Scribed by Henk Broer; Carles Simó
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 388 KB
- Volume
- 166
- Category
- Article
- ISSN
- 0022-0396
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📜 SIMILAR VOLUMES
We consider the problem u + u p + u q = 0, in R N 0 < u(x) → 0 as |x| → +∞, where 1 < p < (N + 2)/(N -2) < q. We prove that if q is fixed and we let p approach (N + 2)/(N -2) from below, then this problem has a large number of radial solutions. A similar fact takes place if we fix p > N/(N -2) and t
The variational equation of the periodic solution in an homogenous potential of degree 2m leads to a family of Hill's equations. H. Yoshida solves these equations by a transformation to the Gauss equation of hypergeometric functions. We study directly this family for complex t, and in the case m ---