Geodesic
Periodic solutions of a weakly nonlinear hyperbolic equation in $E_2$ and $E_3$
Applications of Mathematics, Tome 19 (1974) no. 4, pp. 232-245.

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For $n=2$ and 3 the existence and uniqueness of classical periodic solution of $\square_nu+2au_t+2(B,\nabla_nu)+cu=h(t,x)+\epsilon f(t,x,u,\epsilon)$ $(x=(x_1, x_2,\ldots,x_n))$ is proved assuming the periodicity of the right-hand side.
DOI : 10.21136/AM.1974.103537
Classification : 35B10, 35B20, 35L60 
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     title = {Periodic solutions of a weakly nonlinear hyperbolic equation in $E_2$ and $E_3$},
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Vítek, Václav. Periodic solutions of a weakly nonlinear hyperbolic equation in $E_2$ and $E_3$. Applications of Mathematics, Tome 19 (1974) no. 4, pp. 232-245. doi : 10.21136/AM.1974.103537. http://geodesic.mathdoc.fr/articles/10.21136/AM.1974.103537/

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