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I need some guidance with a problem in the calculus of variations. I want to use direct methods to prove the existence of a minimizer of a certain functional, but I don't really know what I'm doing. If anyone with expertise is reading, I've given a full description at MathOverflow.
I think Minimax methods in critical point theory with applications to differential equations by Paul Rabinowitz might help me out.
You can download the book here.
Thanks!