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Asymptotic behavior of solutions to the perturbed simple pendulum problems with two parameters

✍ Scribed by Tetsutaro Shibata

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
141 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We consider the perturbed simple pendulum equation

–u β€³(t) + ΞΌ |u (t)|^p –1^u (t) = Ξ» sin u (t), t ∈ I ≔ (–T, T),

u (t) > 0, t ∈ I,

u (Β±T) = 0,

where p > 1 is a constant,Ξ» > 0 and ΞΌ ∈ R are parameters. The purpose of this paper is to clarify the structure of the solution set. To do this, we study precisely the asymptotic shape of the solutions when Ξ» ≫ 1 as well as the asymptotic behavior of variational eigenvalue ΞΌ (Ξ») as Ξ» β†’ ∞. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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