Layer structures for the solutions to the perturbed simple pendulum problems

Journal of Mathematical Analysis and Applications Volume 315 Issue 2 Page 725-739 published_at 2006

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Title ( eng )	Layer structures for the solutions to the perturbed simple pendulum problems
Creator	Shibata Tetsutaro
Source Title	Journal of Mathematical Analysis and Applications
Volume	315
Issue	2
Start Page	725
End Page	739
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.
Keywords	Boundary layer Interior layer Simple pendulum problems
NDC	Mathematics [ 410 ]
Language	eng
Resource Type	journal article
Publisher	Elsevier Inc
Date of Issued	2006
Rights	Copyright (c) 2006 Elsevier Inc
Publish Type	Author’s Original
Access Rights	open access
Source Identifier	[DOI] 10.1016/j.jmaa.2005.06.049 [ISSN] 0022-247X [NCID] AA00252847 [DOI] http://dx.doi.org/10.1016/j.jmaa.2005.06.049 isVersionOf