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