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__a280,
     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__a280/}
}
TY  - JOUR
AU  - Shibata,  Tetsutaro
TI  - Asymptotic shape of solutions to the perturbed simple pendulum problems
JO  - Electronic journal of differential equations
PY  - 2007
VL  - 2007
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a280/
LA  - en
ID  - EJDE_2007__2007__a280
ER  - 
%0 Journal Article
%A Shibata,  Tetsutaro
%T Asymptotic shape of solutions to the perturbed simple pendulum problems
%J Electronic journal of differential equations
%D 2007
%V 2007
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a280/
%G en
%F EJDE_2007__2007__a280
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/