Geodesic
Asymptotic shape of solutions to the perturbed simple pendulum problems
Electronic journal of differential equations, Tome 2007 (2007)
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 
@article{EJDE_2007__2007__a180,
     author = {Shibata,  Tetsutaro},
     title = {Asymptotic shape of solutions to the perturbed simple pendulum problems},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1133.35363},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a180/}
}
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%A Shibata,  Tetsutaro
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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__a180/