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While studying calculus of variations, there is one question that I feel is missing in the texts I'm reading:

What can we say about the existence and/or uniqueness of solutions to Euler-Lagrange equations? Is there any general result?

I tried to google it, but found nothing.Thanks in advance

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Results about existence/uniqueness of solution to Euler-Lagrange equations?

While studying calculus of variations, there is one question that I feel is missing in the texts I'm reading:

What can we say about the existence and/or uniqueness of solutions to Euler-Lagrange equations? Is there any general result?

I tried to google it, but found nothing. Thanks in advance