Geodesic
Periodic solutions of a weakly nonlinear wave equation in $E_3$ in a spherically symmetrical case
Applications of Mathematics, Tome 14 (1969) no. 2, pp. 160-167
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the paper the conditions for the existence of a $2\pi$-periodic solution in $t$ of the system $u_{tt}-u_{rr}-(2/r)u_r=\epsilon f(t,r,u,u_t,u_r)$, $\left|u(t,0)\right|+\infty,\ u(t,\pi)=0$ are investigated provided that $f$ is sufficiently smooth and $2\pi$-periodic in $t$.
In the paper the conditions for the existence of a $2\pi$-periodic solution in $t$ of the system $u_{tt}-u_{rr}-(2/r)u_r=\epsilon f(t,r,u,u_t,u_r)$, $\left|u(t,0)\right|+\infty,\ u(t,\pi)=0$ are investigated provided that $f$ is sufficiently smooth and $2\pi$-periodic in $t$.
DOI : 10.21136/AM.1969.103218
Classification : 35-12
Keywords: partial differential equations 
@article{10_21136_AM_1969_103218,
     author = {Vejvoda, Otto},
     title = {Periodic solutions of a weakly nonlinear wave equation in $E_3$ in a spherically symmetrical case},
     journal = {Applications of Mathematics},
     pages = {160--167},
     year = {1969},
     volume = {14},
     number = {2},
     doi = {10.21136/AM.1969.103218},
     mrnumber = {0239247},
     zbl = {0175.39504},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103218/}
}
TY  - JOUR
AU  - Vejvoda, Otto
TI  - Periodic solutions of a weakly nonlinear wave equation in $E_3$ in a spherically symmetrical case
JO  - Applications of Mathematics
PY  - 1969
SP  - 160
EP  - 167
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103218/
DO  - 10.21136/AM.1969.103218
LA  - en
ID  - 10_21136_AM_1969_103218
ER  - 
%0 Journal Article
%A Vejvoda, Otto
%T Periodic solutions of a weakly nonlinear wave equation in $E_3$ in a spherically symmetrical case
%J Applications of Mathematics
%D 1969
%P 160-167
%V 14
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103218/
%R 10.21136/AM.1969.103218
%G en
%F 10_21136_AM_1969_103218
Vejvoda, Otto. Periodic solutions of a weakly nonlinear wave equation in $E_3$ in a spherically symmetrical case. Applications of Mathematics, Tome 14 (1969) no. 2, pp. 160-167. doi: 10.21136/AM.1969.103218

[1] O. Vejvoda: Periodic solutions of a linear and weakly nonlinear wave equation in one dimension, I. Czechoslovak Math. Journal, 14 (89), 1964, 341-382. | MR

Cité par Sources :