dc.contributor.author Shibata, Tetsutaro ( ) dc.date.accessioned 2021-08-06T18:24:16Z dc.date.available 2021-08-06T18:24:16Z dc.date.issued 2007-05-09 dc.identifier.citation Shibata, T. (2007). Asymptotic shape of solutions to the perturbed simple pendulum problems. Electronic Journal of Differential Equations, 2007(64), pp. 1-11. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/14226 dc.description.abstract We 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.format Text dc.format.extent 11 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University-San Marcos, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Asymptotic formulas en_US dc.subject Lq-norm en_US dc.subject Simple pendulum en_US dc.title Asymptotic shape of solutions to the perturbed simple pendulum problems en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
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