Geodesic
Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions
Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1064-1086

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We prove the existence of a countable family of time-periodic solutions of the quasilinear equation of beam vibrations with homogeneous boundary conditions and time-periodic right-hand side in the case when the non-linear term has power growth.
Keywords: beam vibrations, time-periodic solution, variational method, perturbation of even functionals. 
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     author = {I. A. Rudakov},
     title = {Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions},
     journal = {Izvestiya. Mathematics },
     pages = {1064--1086},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a8/}
}
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I. A. Rudakov. Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions. Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1064-1086. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a8/