Results 1 to 10 of about 343 (158)

The strong Ekeland variational principle

Journal of Mathematical Analysis and Applications, 2006
The main purpose of the present paper is to establish an extension of Ekeland's variational principle. The author is mainly concerned with quasiconvex proper and lower semicontinuous functions defined on a reflexive Banach space. In the last part of the paper this result is generalized in the framework of compact metric spaces endowed with a \(\tau ...
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A Set-Valued Ekeland's Variational Principle in Vector Optimization

SIAM Journal on Control and Optimization, 2008
This paper deals with Ekeland's variational principle for vector optimization problems. By using a set-valued metric, a set-valued perturbed map, and a cone-boundedness concept based on scalarization, we introduce an original approach to extending the well-known scalar Ekeland's principle to vector-valued maps.
César Gutiérrez, Bienvenido Jiménez, Vicente Novo   +2 more
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Multiple solutions of a p-Kirchhoff equation with singular and critical nonlinearities

Electronic Journal of Differential Equations, 2017
In this article, we explore the existence of multiple solutions for a p-Kirchhoff equation with the nonlinearity containing both singular and critical terms.
Qin Li, Zuodong Yang, Zhaosheng Feng
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A generalization of the Ekeland variational principle

, 2020
In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving the second Gâteaux variation of the functional in question.
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Maximum principle for delayed stochastic mean-field control problem with state constraint

Advances in Difference Equations, 2019
In this paper, we consider the optimal control problem for the mean-field stochastic differential equations with delay and state constraint. By virtue of the classical Ekeland’s variational principle, the duality method and a new type of mean-field ...
Li Chen, Jiandong Wang
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Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian

Advances in Mathematical Physics, 2015
We study the existence of weak solutions to the following Neumann problem involving the p(x)-Laplacian operator:  -Δp(x)u+e(x)|u|p(x)-2u=λa(x)f(u), in  Ω, ∂u/∂ν=0, on  ∂Ω.
Qing Miao
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The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces

Mathematics, 2023
Roughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space. Later, Pando Georgiev (J. Math. Anal. Appl. 131 (1988), no. 1, 1–21) and Tomonari Suzuki (J. Math. Anal. Appl.
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Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

Mathematics, 2018
We consider a distance function on generalized metric spaces and we get a generalization of Ekeland Variational Principle (EVP). Next, we prove that EVP is equivalent to Caristi–Kirk fixed point theorem and minimization Takahashi’s theorem.
Eshagh Hashemi, Reza Saadati
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An Ekeland’s variational principle for set-valued mappings with applications

Journal of Computational and Applied Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zeng, J., Li, S.J.
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Concerning Kirk’s problem

Fixed Point Theory and Algorithms for Sciences and Engineering
This paper presents a straightforward statement for Khamsi’s theorem without assuming continuity or nondecreasing restrictions on η. Additionally, a new proof provides an affirmative answer to Kirk’s problem, supported by examples.
Hamid Mottaghi Golshan
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