Periodic solutions of nonlinear wave equations with non-monotone forcing terms (Q2504803)

Summary: 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 \textit{P. Rabinowitz} [Commun. Pure Appl. Math. 20, 145--205 (1967; Zbl 0152.10003)].