2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168689We investigate the cubic defocusing fourth order Schrödinger equation $iu_t + Δ^2u + |u|^2u=0$ in arbitrary space dimension $\mathbb{R}^n$ for arbitrary $H^2$ initial data. We prove that the equation is globally well-posed when $n \le 8$ and ill-posed when $n \ge 9$, with the additional important information that scattering holds true when $5 \le n \le 8$.38 pages, references addedAnalysis of PDEs35Q40; 35Q55text