2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66408Let $F$ be a nonlinear Frechet differentiable map in a real Hilbert space. Condition sufficient for existence of a solution to the equation $F(u)=0$ is given, and a method (dynamical systems method, DSM) to calculate the solution as the limit of the solution to a Cauchy problem is justified under suitable assumptions.Dynamical Systems37C35, 37L05, 37N30, 47H15, 58C15, 65J15text