This paper is concerned with the perturbed simple pendulum problem -u"(t)+g(u(t)) = λsinu(t), u{t) > 0, t ∈I: = =(-T,T), u(±T) = 0, where λ > 0 is a parameter. It is known that if λ 1, then the corresponding solution develops the boundary layers. We adopt a new parameter ε ∈ (0,T) which characterizes both the boundary layers and the height of the solution and parametrize a solution pair (λ,u) by ∈, namely, (λ,u) = (λ(ε),u_ε), and establish the three-term asymptotics for λ(ε) as ε → 0.
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