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Exponential Dichotomies by Ekeland’s Variational Principle
Journal of Dynamics and Differential Equations, 2020Exponential dichotomy, which is a type of hyperbolicity in the context of linear time-varying systems, is the central focus of this paper. First, two well known characterizations of the exponential dichotomy in \(\mathbb{R}^+\) are presented: \begin{itemize} \item [(i)] If the system \(\dot{v}=A(t)v+f(t)\) in \(\mathbb{R}^N\), admits a bounded solution
Juan Campos, Massimo Tarallo
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Ekeland Variational Principles in Vector Equilibrium Problems
SIAM Journal on Optimization, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
César Gutiérrez +3 more
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2014
In this chapter we present existence results for minimal points of subsets of the Cartesian product of a complete metric space and a topological vector space with respect to order relations determined by generalized set-valued metrics; such results are useful for deriving EVP type results for vector and scalar functions.
Akhtar A. Khan +2 more
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In this chapter we present existence results for minimal points of subsets of the Cartesian product of a complete metric space and a topological vector space with respect to order relations determined by generalized set-valued metrics; such results are useful for deriving EVP type results for vector and scalar functions.
Akhtar A. Khan +2 more
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On generalizations of the Ekeland-type variational principles
Nonlinear Analysis: Theory, Methods & Applications, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Ekeland's Variational Principle for Set-Valued Mappings
Acta Mathematicae Applicatae Sinica, English Series, 2007Let \(X\) be a complect metric space and \(E\) be an ordered Hausdorff topological vector space. In this paper for new classes of set valued mappings \(F:X \rightarrow 2^{E}\) the vector Ekeland's variation principle is proved.
Li, Sheng-Jie, Zhang, Wen-Yan
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Vector Ekeland Variational Principle
2000In this paper the well-known Ekeland variational principle is generalized to the case where vector-valued functions are involved. Namely, vector Ekeland variational principle is studied. In particular, the epsilon vector minimum point of a vector optimization problem is investigated via vector Ekeland variational principle.
Shen Jie Li, Xiao Qi Yang, Guang-ya Chen
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The Brezis–Ekeland Principle for Doubly Nonlinear Equations
SIAM Journal on Control and Optimization, 2008The celebrated Brezis-Ekeland principle [C. R. Acad. Sci. Paris Ser. A-B, 282 (1976), pp. Ai, A1197-A1198, Aii, and A971-A974] characterizes trajectories of nonautonomous gradient flows of convex functionals as solutions to suitable minimization problems.
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Ekeland’s variational principle with weighted set order relations
Mathematical Methods of Operations Research, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qamrul Hasan Ansari +2 more
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