Results 31 to 40 of about 512 (163)
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 We are concerned with the following nonlocal problem involving critical Sobolev exponent −a−b∫Ω∇u2dxΔu=λuq−2u+δu2u,x∈Ω,u=0,x∈∂Ω, where Ω is a smooth bounded domain in ℝ4, a, b > 0, 1 < q < 2, δ, and λ are positive parameters. We prove the existence of two positive solutions and obtain uniform estimates of extremal values for the problem.
Zhigao Shi, Xiaotao Qian, Simone Secchi
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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 for Set-Valued Functions [PDF]
SIAM Journal on Optimization, 2011 The authors extend Ekeland's variational principle to the case of set-valued mappings by using a set of directions and some particular partial orders related to it. Then, as an application they establish some sufficient conditions for the existence of an error bound of a finite system of inequalities of lower semicontinuous functions on a Banach space.
Liu, C. G., Ng, K. F.
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Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces
Abstract and Applied Analysis, 2012 Some new vectorial Ekeland variational principles in cone quasi-uniform spaces are proved. Some new equivalent principles, vectorial quasivariational inclusion principle, vectorial quasi-optimization principle, vectorial quasiequilibrium principle are ...
Jiang Zhu +3 more
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Abstract and Applied Analysis, 2011 By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium ...
Wei-Shih Du
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The Multiplicity of Nontrivial Solutions for a New px-Kirchhoff-Type Elliptic Problem
Journal of Function Spaces, 2021 In the paper, we study the existence of weak solutions for a class of new nonlocal problems involving a px-Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, we prove that the new px-Kirchhoff problem has at least two
Chang-Mu Chu, Yu-Xia Xiao
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Epsilon Solutions and Duality in Vector Optimization [PDF]
, 1987 This paper is a continuation of the author's previous investigations in the theory of epsilon-solutions in convex vector optimization and serves as a theoretical background for the research of SDS in the field of multicriteria optimization.
Valyi, I.
core +1 more source
Existence of equilibria via Ekeland's principle
Journal of Mathematical Analysis and Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bianchi, Monica +2 more
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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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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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