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ID 15347
file
creator
subject
Boundary layer
Interior layer
Simple pendulum problems
NDC
Mathematics
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.
journal title
Journal of Mathematical Analysis and Applications
volume
Volume 315
issue
Issue 2
start page
725
end page
739
date of issued
2006
publisher
Elsevier Inc
issn
0022-247X
ncid
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
author
rights
Copyright (c) 2006 Elsevier Inc
relation is version of URL
http://dx.doi.org/10.1016/j.jmaa.2005.06.049
department
Graduate School of Engineering