2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73044We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of RabinowitzAnalysis of PDEs35L05, 35L20, 35B10, 37K10text