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

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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]. 
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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},
     publisher = {mathdoc},
     volume = {Ser. 9, 16},
     number = {2},
     year = {2005},
     zbl = {1225.35147},
     mrnumber = {MR2225505},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a3/}
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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/