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2004 Three-term spectral asymptotics for the perturbed simple pendulum problems
Tetsutaro Shibata
Differential Integral Equations 17(1-2): 215-226 (2004).

Abstract

This paper is concerned with the perturbed simple pendulum problem $$ -u''(t) + g(u(t)) = \lambda \sin u(t), \ \ u(t) > 0, \ \ t \in I := (-T, T), \ \ u(\pm T) = 0, $$ where $\lambda > 0$ is a parameter. It is known that if $\lambda \gg 1$, then the corresponding solution develops the boundary layers. We adopt a new parameter $\epsilon \in (0, T)$ which characterizes both the boundary layers and the height of the solution and parametrize a solution pair $(\lambda, u)$ by $\epsilon$, namely, $(\lambda, u) = (\lambda(\epsilon), u_\epsilon),$ and establish the three-term asymptotics for $\lambda(\epsilon)$ as $\epsilon \to 0$.

Citation

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Tetsutaro Shibata. "Three-term spectral asymptotics for the perturbed simple pendulum problems." Differential Integral Equations 17 (1-2) 215 - 226, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1164.34450
MathSciNet: MR2035503

Subjects:
Primary: 34B15

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 1-2 • 2004
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