Ramos del Olmo, Ángel ManuelHenry, J.2023-06-202023-06-202008-05-150362-546X10.1016/j.na.2007.02.040https://hdl.handle.net/20.500.14352/49622In [J. Henry, A.M. Ramos, Factorization of second order elliptic boundary value problems by dynamic programming, Nonlinear Analysis. Theory, Methods & Applications 59 (2004) 629–647] we presented a method for factorizing a second-order boundary value problem into a system of uncoupled first-order initial value problems, together with a nonlinear Riccati type equation for functional operators. A weak sense was given to that system but we did not perform a direct study of those equations. This factorization utilizes either the Neumann to Dirichlet (NtD) operator or the Dirichlet to Neumann (DtN) operator, which satisfy a Riccati equation. Here we consider the framework of Hilbert–Schmidt operators, which provides tools for a direct study of this Riccati type equation. Once we have solved the system of Cauchy problems, we show that its solution solves the original second-order boundary value problem. Finally, we indicate how this techniques can be used to find suitable transparent conditions.engStudy of the Initial Value Problems Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problemsjournal articlehttp://www.sciencedirect.com/science/journal/0362546Xopen access517.986.6517.518.45FactorizationBoundary value problemHilbert–Schmidt operatorRiccati equationInvariant embeddingNeumann to Dirichlet (NtD) operatorDirichlet to Neumann (DtN) operatorTransparent conditionsAnálisis matemático1202 Análisis y Análisis Funcional