Let $I$ be a real functional over a Hilbert space $H$, satisfying all the conditions in the Mountain pass (M-P) theorem. My question is, can the assumption in the M-P theorem that $I[v]\leq 0$ for a $v$ such that $||v||=r$ be replaced by simply $I[v]=0$?. I think the $<$ zero is redundant.
2026-04-02 17:03:02.1775149382
Mountain pass theorem
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