I'd like to read your opinions on the following question.
Assume one want to translate in English the following sentence:
Siano \(f,g\) funzioni tali che [qualche proprietà].
Allora esistono funzioni \(u\) di classe \(C^1\) che risolvono [un problema].
My tentative translation is:
"Let \(f,g\) functions such that [some property].
Then, there exist functions \(u\) of class \(C^1\) which solve [a problem]"
where the verb to exist agrees with the noun functions (which it refers to).
Nevethless, someone came up with the following correction to my translation:
"Let \(f,g\) functions such that [some property].
Then, there exists functions \(u\) of class \(C^1\) which solve [a problem]"
where the verb to exist is in third singular person (I assume it's a sort of an impersonal construction).
In your opinion, which translation in the (most) correct one?
Or, maybe, do you like something as:
"Let \(f,g\) functions such that [some property].
Then, there exists at least one function \(u\) of class \(C^1\) which solves [a problem]"
(a sort of compromise)?
