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Measuring restoration quality in urban forest greenways: insights for planning and management. [PDF]
Front PsycholWang H, Liu Y, Zhang MJ, Wang X.
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A Mountain Pass to the Jacobian Conjecture
Canadian Mathematical Bulletin, 1998AbstractThis paper presents an approach to injectivity theorems via the Mountain Pass Lemma and raises an open question. The main result of this paper (Theorem 1.1) is proved by means of the Mountain Pass Lemma and states that if the eigenvalues of are uniformly bounded away from zero for x ∊ Rn, where is a class C1 map, then F is injective. This was
Chamberland, Marc, Meisters, Gary
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2021
This chapter focuses on Stanisław Witkiewicz, who largely contributed to the discovery and popularity of Zakopane. However, he credited Chałubiński for the discovery of the Tatras. The Jewish presence in Zakopane was viewed differently by various parties to the highland encounter.
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This chapter focuses on Stanisław Witkiewicz, who largely contributed to the discovery and popularity of Zakopane. However, he credited Chałubiński for the discovery of the Tatras. The Jewish presence in Zakopane was viewed differently by various parties to the highland encounter.
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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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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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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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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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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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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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