2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94512We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical partial differential equations to a system of ordinary differential equations, and provide a nonlinear counterpart to quasi-exactly solvable quantum Hamiltonians. These results rely on a useful extension of the classical Wronskian determinant condition for linear independence of functions. In addition, new approaches to the characterization o f the annihilating differential operators for spaces of analytic functions are presented.28 pages. To appear in Advances in MathematicsExactly Solvable and Integrable Systemstext