Geodesic
On the existence of periodic solutions of semilinear elliptic equations
Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 167-178

Voir la notice de l'article provenant de la source Math-Net.Ru

Using a variational method, the existence is proved of a solution of the equation $-\Delta u=g(u)$ in $\mathbb{R}^{N+1}$, periodic with respect to one variable and localized with respect to the remaining variables. 
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     author = {Ya. Sh. Il'yasov},
     title = {On the existence of periodic solutions of semilinear elliptic equations},
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Ya. Sh. Il'yasov. On the existence of periodic solutions of semilinear elliptic equations. Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 167-178. http://geodesic.mathdoc.fr/item/SM_1994_79_1_a10/