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On the sign of the mountain pass solution
Nonlinear Analysis: Theory, Methods & Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Costa, D. G., Tehrani, H.
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2007
Roughly speaking, the basic idea behind the so-called minimax method is the following: Find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ℝ of ϕ over a suitable class A of subsets of X: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$
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Roughly speaking, the basic idea behind the so-called minimax method is the following: Find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ℝ of ϕ over a suitable class A of subsets of X: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$
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A Variation of the Mountain Pass Lemma and Applications
Journal of the London Mathematical Society, 1991This paper studies functionals \(f\in C^ 1(H,\mathbb{R})\) \((H\)-Hilbert space) satisfying the conditions of the mountain pass lemma with the exception of the PS condition. The author was able to find \(c\in\mathbb{R}\) such that for any rapidly decreasing function \(\psi:\mathbb{R}_ +\to\mathbb{R}_ +\) there is a sequence \((u_ j)\subset H ...
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2003
This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a ...
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This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a ...
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Minimization and Mountain-Pass Theorems
2001In this introductory chapter, we consider the concept on differentiability of mappings in Banach spaces, Frechet and Gâteaux derivatives, secondorder derivatives and general minimization theorems. Variational principles of Ekeland [Ek1] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais—
Maria do Rosário Grossinho +1 more
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Mountain Passes in Epicnemidian Locris
2013Mountain passes are a structural element in the Locrian landscape and at the same time the scene of famous chapters in history. At various points in this monograph it has been commented that the rugged profile of this region, added to the limitations imposed by the northern seaboard, make the irregular longitudinal valleys, the high plateaus to the ...
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A Generalized Mountain Pass Theorem
20202010 Mathematics Subject Classification: 58E05, 58E30.
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Truck Safety Evaluation on Wyoming Mountain Passes
Accident Analysis and Prevention, 2019Milhan Moomen +2 more
exaly