Geodesic
Periodic solutions of nonlinear wave equations with non-monotone forcing terms
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 2, pp. 117-124

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Zbl   MR

Existence and regularity of periodic solutions of nonlinear, completely resonant, forced wave equations is proved for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. The corresponding infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. This difficulty is overcome finding a-priori estimates for the constrained minimizers of the reduced action functional, through techniques inspired by regularity theory as in [10]. 
Berti, Massimiliano; Biasco, Luca. Periodic solutions of nonlinear wave equations with non-monotone forcing terms. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 2, pp. 117-124. http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a3/
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     author = {Berti, Massimiliano and Biasco, Luca},
     title = {Periodic solutions of nonlinear wave equations with non-monotone forcing terms},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {117--124},
     year = {2005},
     volume = {Ser. 9, 16},
     number = {2},
     zbl = {1225.35147},
     mrnumber = {MR2225505},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a3/}
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