Given an equation (e.g., a PDE), is there any way to determine if it is an Euler-Lagrange equation of some functional?
If yes, is there in general any method to find out the functional? Or must there be any additional assumption for this to be true?
If no, what is the best we can say about it? For example, is is possible to say about how close or far from being an Euler-Lagrange equation?
Any question is welcomed, since I am aware that my questions may be too vague.
Thanks for any answer and suggestion on references.