Geodesic
Absence of time-periodic solutions to certain multidimensional nonlinear wave equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 152 (1986), pp. 55-66

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In this paper 1 give some tests for the absence of time-periodic (and vanishing at the space infinity) solutions to the nonlinear wave equations of the form $\square u=F(u)$. 
@article{ZNSL_1986_152_a5,
     author = {L. V. Kapitanski},
     title = {Absence of time-periodic solutions to certain multidimensional nonlinear wave equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--66},
     publisher = {mathdoc},
     volume = {152},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_152_a5/}
}
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L. V. Kapitanski. Absence of time-periodic solutions to certain multidimensional nonlinear wave equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 152 (1986), pp. 55-66. http://geodesic.mathdoc.fr/item/ZNSL_1986_152_a5/