Results 181 to 190 of about 38,310 (232)
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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: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$
D. Costa
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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: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$
D. Costa
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p-Laplacian Type Equations Via Mountain Pass Theorem in Cerami Sense
Qualitative Theory of Dynamical SystemsJ. Vanterler da C. Sousa +2 more
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An alternative proof of the mountain pass theorem for a class of functionals
Journal of Global Optimization, 2013The authors present an alternative proof of the well known mountain pass theorem by the use of the Ekeland variational principle for a class of \(C^1\)-functionals.
M. Montenegro, A. E. Presoto
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Complex Variables and Elliptic Equations, 2021
In this paper, we consider the following quasilinear equation: where M is a compact Riemannian manifold with dimension without boundary, and . Here , and are continuous functions on M satisfying some further conditions.
Yuh-ching Chen, Nanbo Chen, Xiaochun Liu
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In this paper, we consider the following quasilinear equation: where M is a compact Riemannian manifold with dimension without boundary, and . Here , and are continuous functions on M satisfying some further conditions.
Yuh-ching Chen, Nanbo Chen, Xiaochun Liu
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Morse indices at critical points related to the symmetric mountain pass theorem and applications
, 1989 Kazunaga Tanaka
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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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A Strong Form of the Mountain Pass Theorem and Application
, 1988 Variational methods are a strong tool in proving existence of solutions of differential equations. In this paper we prove a strong form of the mountain pass theorem which was prompted by the need of a theorem which, besides an existence statement for critical points, gives in addition information about the “fine structure” of the functional near to ...
Helmut Hofer
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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.
Marcello Lucia
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