Asymptotic shape of solutions to the perturbed simple pendulum problems

Date

2007-05-09

Authors

Shibata, Tetsutaro

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

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 → ∞.

Description

Keywords

Asymptotic formulas, Lq-norm, Simple pendulum

Citation

Shibata, T. (2007). Asymptotic shape of solutions to the perturbed simple pendulum problems. Electronic Journal of Differential Equations, 2007(64), pp. 1-11.

Rights

Attribution 4.0 International

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