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A Mountain Pass Theorem and Moduli Space of Minimal Immersions
The Journal of Geometric AnalysisGiven two Banach spaces \(X\) and \(Y\), the author considers functionals \(\mathcal{A}\colon X\times Y\to \mathbb{R}\) of class \(C^1\) which satisfy certain conditions, including that partial maps \(\mathcal{A}(u,\cdot)\) admit a unique minimum for each \(u\in X\), and a weak Palais-Smale condition.
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The Mountain Pass Theorem and Critical Points of Saddle Type
2002In Chapter 9 we shall continue the investigation of the L p solutions of the Hammerstein integral equations under the assumption that f (x, 0) = 0, that is, the null function is a solution. We are now interested in non-null solutions. The technique we use is based on the so called mountain pass theorem of Ambrosetti-Rabinowitz [3].
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Mountain Pass solutions for non-local elliptic operators
Journal of Mathematical Analysis and Applications, 2012Raffaella Servadei, Enrico Valdinoci
exaly
Application of a Variant of Mountain Pass Theorem in Modeling Real Phenomena
Mathematics, 2022exaly