Layer structures for the solutions to the perturbed simple pendulum problems
Use this link to cite this item : https://ir.lib.hiroshima-u.ac.jp/00015347
ID | 15347 |
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creator | |
subject | Boundary layer
Interior layer
Simple pendulum problems
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NDC |
Mathematics
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abstract | 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.
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journal title |
Journal of Mathematical Analysis and Applications
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volume | Volume 315
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issue | Issue 2
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start page | 725
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end page | 739
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date of issued | 2006
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publisher | Elsevier Inc
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issn | 0022-247X
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publisher doi | |
language |
eng
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nii type |
Journal Article
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HU type |
Journal Articles
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DCMI type | text
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format | application/pdf
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text version | author
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rights | Copyright (c) 2006 Elsevier Inc
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relation is version of URL | http://dx.doi.org/10.1016/j.jmaa.2005.06.049
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department |
Graduate School of Engineering
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