e/Nash–Moser theorem

Information
has gloss	eng: The Nash–Moser theorem, attributed to mathematicians John Forbes Nash and Jurgen Moser is a generalization of the inverse function theorem on Banach spaces to a class of "tame" Frechet spaces. In contrast to the Banach space case, in which the invertibility of the derivative at a point is sufficient for a map to be locally invertible, the Nash–Moser theorem requires the derivative to be invertible in a neighborhood. The theorem is widely used to prove local uniqueness for non-linear partial differential equations in spaces of smooth functions.
lexicalization	eng: Nash-Moser theorem
lexicalization	eng: Nash–Moser theorem
instance of	(noun) an equation containing differentials of a function differential equation