2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70955Let $L$ be an unbounded linear operator in a real Hilbert space $H$, a generator of $C_0$ semigroup, and $g:H\to H$ be a $C^2_{loc}$ nonlinear map. The DSM (dynamical systems method) for solving equ$ $F(v):=Lv+gv=0$ consists of solving the Cauchy problem $\dot {u}=Φ(t,u)$, $u(0)=u_0$, where $Φ$ is a suitable operator, and proving that i) $\exists u(t) \quad \forall t>0$, ii) $\exists u(\infty)$, and iii) $F(u(\infty))=0$.Functional Analysis35R25, 35R30, 37B55, 47H20, 47J05, 49N45, 65M32, 65R30text