On the variational principle
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The variational principle states that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F'(uJj* < l, i.e., its derivative can be made arbitrarily small as discussed by the authors.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1974-08-01 and is currently open access. It has received 2105 citations till now. The article focuses on the topics: Differentiable function & Variational principle.read more
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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
Haim Brezis,Louis Nirenberg +1 more
TL;DR: In this article, the existence of a fonction u satisfaisant l'equation elliptique non lineaire is investigated, i.e., a domaine borne in R n avec n ≥ 3.
Book
Convex analysis and nonlinear optimization : theory and examples
TL;DR: In this paper, the Karush-Kuhn-Tucker Theorem and Fenchel duality were used for infinite versus finite dimensions, with a list of results and notation.
Book ChapterDOI
Theory of Vector Optimization
Christiane Tammer,Alfred Göpfert +1 more
TL;DR: This work derives necessary and sufficient optimality conditions, a minimal point theorem, a vector-valued variational principle of Ekeland’s type, Lagrangean multiplier rules and duality statements, and discusses a general scalarization procedure.
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Nonconvex minimization problems
TL;DR: In this paper, it was shown that the set of continuous linear functionals on a Banach space E which attain their maximum on a prescribed closed convex bounded subset X c E is norm-dense in £ *.
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On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
TL;DR: In this paper, the authors derive a generic theorem for a wide class of functionals, having a mountain pass geometry, and show how to obtain, for a given functional, a special Palais-Smale sequence possessing extra properties that help to ensure its convergence.
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