Results 41 to 50 of about 1,231,124 (145)
Ekeland's variational principle in locally convex spaces and the density of extremal points [PDF]
, 2009 In this paper, we prove a general version of Ekeland's variational principle in locally convex spaces, where perturbations contain subadditive functions of topology generating seminorms and nonincreasing functions of the objective function. From this, we
Qiu, Jing-Hui
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this article, multiplicity of nontrivial solutions for an inhomogeneous singular biharmonic equation with Rellich potential are studied. Firstly, a negative energy solution of the studied equations is achieved via the Ekeland's variational principle ...
Yang Yu, Yulin Zhao
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One remark to Ekeland's variational principle [PDF]
, 1997 This article deals with the generalization of Ekeland's first-order necessary conditions of minimum. They are extended to include second-order conditions.
Bobylev, N. +5 more
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On Ekeland’s Variational Principle in Rectangular bmertic Spaces
Journal of Harbin University of Science and Technology, 2020 Ekeland′s variational principle plays an important role in fixed point theory. It has applications in many fields such as optimization theory, control theory, critical point theory and others.
HUANG Shuai, CHEN Lili, LIU Xin
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Ekeland’s variational principle with weighted set order relations
Mathematical Methods of Operations Research, 2019 The main results of the paper are a minimal element theorem and an Ekeland-type variational principle for set-valued maps whose values are compared by means of a weighted set order relation. This relation is a mixture of a lower and an upper set relation
Q. Ansari, A. Hamel, P. K. Sharma
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Maximum principle for near-optimality of stochastic delay control problem
Advances in Difference Equations, 2017 This paper is concerned with near-optimality for stochastic control problems of linear delay systems with convex control domain and controlled diffusion. Necessary and sufficient conditions for a control to be near-optimal are established by Pontryagin’s
Feng Zhang
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Some new results on stability of Ekeland's ϵ-variational principle [PDF]
, 2008 In this paper, we give an example and point out that ϵ-solutions of Ekeland's variational principle are not always lower semicontinuous in infinite-dimensional Banach spaces, even with respect to the uniform metric.
Wang, Changchun +2 more
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Critical point result of Schechter type in a Banach space
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Using Ekeland's variational principle we give a critical point theorem of Schechter type for extrema on a sublevel set in a Banach space. This result can be applied to localize the solutions of PDEs which contain nonlinear homogeneous operators.
Hannelore Lisei, Orsolya Vas
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International Journal of Differential Equations, 2015 We consider the existence of nontrivial solutions to elliptic equations with decaying cylindrical potentials and subcritical exponent. We will obtain a local minimizer by using Ekeland’s variational principle.
Mohammed El Mokhtar Ould El Mokhtar
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A minimization theorem in quasi-metric spaces and its applications
International Journal of Mathematics and Mathematical Sciences, 2002 We prove a new minimization theorem in quasi-metric spaces, which improves the results of Takahashi (1993). Further, this theorem is used to generalize Caristi's fixed point theorem and Ekeland's ϵ-variational principle.
Jeong Sheok Ume
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