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
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 $\lambda \to \infty$.
| $ u''(r) + \frac{N-1}{r}u'(r) - g(u(t)) + \lambda \sin u(r) = 0, $ |
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__a80/
@article{EJDE_2007__2007__a80,
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__a80/}
}