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Exploring the Potential of Machine Learning Algorithms Associated with the Use of Inertial Sensors for Goat Kidding Detection. [PDF]
Animals (Basel)Gonçalves P +6 more
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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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p-Laplacian Type Equations Via Mountain Pass Theorem in Cerami Sense
Qualitative Theory of Dynamical SystemszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vanterler da C. Sousa, J. +2 more
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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 pass theorems without Palais–Smale conditions
Journal of Mathematical Sciences, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Application of a Mountain Pass Theorem
Acta Mathematica Sinica, English Series, 2002The present paper is devoted to study the following Dirichlet problem: \[ -\Delta u=f(x,u), \quad x\in\Omega,\;u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^N\), with \(f(x,t)\) asymptotically linear in \(t\) at infinity.
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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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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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