2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103746We study the periodical solutions of a Poisson-gradient PDEs system with bounded nonlinearity. Section 1 introduces the basic spaces and functionals. Section 2 studies the weak differential of a function and establishes an inequality. Section 3 formulates some conditions under which the action functional is continuously differentiable. Section 4 analyzes the Poisson-gradient systems and some conditions that ensure periodical solutions.15 pagesDynamical SystemsAnalysis of PDEs35J50, 35J55text