Shibata, Tetsutaro2021-08-062021-08-062007-05-09Shibata, T. (2007). Asymptotic shape of solutions to the perturbed simple pendulum problems. <i>Electronic Journal of Differential Equations, 2007</i>(64), pp. 1-11.1072-6691https://hdl.handle.net/10877/14226We 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 → ∞.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalAsymptotic formulasLq-normSimple pendulumArticle