2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161980We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.Functional Analysis47B99; 35J60; 46B99; 47N20text