2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106431The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an inhomogeneous wave equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the periods must satisfy to ensure the solvability of the inhomogeneous wave equation by a smooth periodic function. To derive this information, a complete metric theory for a related fully nonlinear Diophantine approximation problem involving perfect squares is established.20 pagesAnalysis of PDEsNumber Theory35L05 (Primary); 11J83, 11J13, 11K60 (Secondary)text