Geodesic
Asymptotic shape of solutions to the perturbed simple pendulum problems
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the positive solution of the perturbed simple pendulum problem $$ u''(r) + \frac{N-1}{r}u'(r) - g(u(t)) + \lambda \sin u(r) = 0, $$ with $0 less than r less than R, u'(0) = u(R) = 0$. To understand well the shape of the solution $u_\lambda$ when $\lambda \gg 1$, we establish the leading and second terms of $\Vert u_\lambda\Vert_q (\lambda \to \infty$. We also obtain the asymptotic formula for $u_\lambda'(R)$ as $\lambda \to \infty$.
Classification : 35J60
Keywords: asymptotic formulas, lq-norm, simple pendulum 
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     author = {Shibata, Tetsutaro},
     title = {Asymptotic shape of solutions to the perturbed simple pendulum problems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a280/}
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Shibata, Tetsutaro. Asymptotic shape of solutions to the perturbed simple pendulum problems. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a280/