Asymptotic shape of solutions to the perturbed simple pendulum problems

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dc.contributor.authorShibata, Tetsutaro
dc.date.accessioned2021-08-06T18:24:16Z
dc.date.available2021-08-06T18:24:16Z
dc.date.issued2007-05-09
dc.description.abstractWe consider the positive solution of the perturbed simple pendulum problem u″(r) + N - 1/r u′(r) - g(u(t)) + λ sin u(r) = 0, with 0 < r < R, u′(0) = u(R) = 0. To understand well the shape of the solution uλ when λ ≫ 1, we establish the leading and second terms of ∥uλ∥q (1 ≤ q < ∞) with the estimate of third term as λ → ∞. We also obtain the asymptotic formula for u′λ(R) as λ → ∞.
dc.description.departmentMathematics
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationShibata, T. (2007). Asymptotic shape of solutions to the perturbed simple pendulum problems. <i>Electronic Journal of Differential Equations, 2007</i>(64), pp. 1-11.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14226
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectAsymptotic formulas
dc.subjectLq-norm
dc.subjectSimple pendulum
dc.titleAsymptotic shape of solutions to the perturbed simple pendulum problemsen_US
dc.typeArticle

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