Layer structures for the solutions to the perturbed simple pendulum problems

• Shibata, Tetsutaro

抄録

We consider the perturbed simple pendulum equation -u″(t) = μf(u(t)) + λsin u(t), t ∈ I: = (-T, T), u(t) > 0, t ∈ I, u(±T) = 0, where λ > 0 and μ ∈ R are parameters. The typical example of f is f(u) = u p-1u(p > 1). The purpose of this paper is to study the shape of the solutions when λ ≫ 1. More precisely, by using a variational approach, we show that there exist two types of solutions: one is almost flat inside I and another is like a step function with two steps.

収録刊行物

• Journal of Mathematical Analysis and Applications

  Journal of Mathematical Analysis and Applications 315 (2), 725-739, 2006

  Elsevier Inc

キーワード

• Boundary layer
• Interior layer
• Simple pendulum problems

詳細情報

• CRID: 1050859215941406208
• NII論文ID: 120000882645
• NII書誌ID: AA00252847
• Web Site: http://ir.lib.hiroshima-u.ac.jp/00015347
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
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  • CiNii Articles
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