Results 71 to 80 of about 2,802 (159)

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

, 2012
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source ...
Aubin J P, Bachmayr M, Brill M, Burger M, Ekeland I, Grasmair M, Grasmair M, Groetsch C W, Hofmann B, K Frick, Krasnosel’skii M A, Krjanev A V, Lardy L J, M Grasmair, Martinet B, Morozov V A, Powell M J D, Scherzer O   +17 more
core   +1 more source

Potential and monotone homeomorphisms in Banach spaces

Advances in Nonlinear Analysis
Using the Ekeland variational principle and the mountain pass lemma we prove some properties about potential homeomorphisms between a real Banach space and its dual.
Bełdziński Michał, Galewski Marek
doaj   +1 more source

Quantitative Characterizations of Regularity Properties of Collections of Sets

, 2014
Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are ...
Kruger, Alexander, Thao, Nguyen Hieu
core   +1 more source

On I. Meghea and C. S. Stamin review article “Remarks on some variants of minimal point theorem and Ekeland variational principle with applications,” Demonstratio Mathematica 2022; 55: 354–379

Demonstratio Mathematica, 2023
Being informed that one of our articles is cited in the paper mentioned in the title, we downloaded it, and we were surprised to see that, practically, all the results from our paper were reproduced in Section 3 of Meghea and Stamin’s article.
Göpfert Alfred, Tammer Christiane, Zălinescu Constantin   +2 more
doaj   +1 more source

Variational Approaches to Characterize Weak Solutions for Some Problems of Mathematical Physics Equations

Abstract and Applied Analysis, 2016
This paper is aimed at providing three versions to solve and characterize weak solutions for Dirichlet problems involving the p-Laplacian and the p-pseudo-Laplacian.
Irina Meghea
doaj   +1 more source

Existence and multiplicity of solutions for nonlocal fourth-order elliptic equations with combined nonlinearities

Boundary Value Problems, 2020
This paper is concerned with the following nonlocal fourth-order elliptic problem: { Δ 2 u − m ( ∫ Ω | ∇ u | 2 d x ) Δ u = a ( x ) | u | s − 2 u + f ( x , u ) , x ∈ Ω , u = Δ u = 0 , x ∈ ∂ Ω , $$\begin{aligned} \textstyle\begin{cases} \Delta ^{2}u-m(\int
Ru Yuanfang, An Yukun
doaj   +1 more source

Existence of solutions for cross critical exponential N-Laplacian systems

Electronic Journal of Differential Equations, 2014
In this article we consider cross critical exponential N-Laplacian systems. Using an energy estimate on a bounded set and the Ekeland variational principle, we prove the existence of a nontrivial weak solution, for a parameter large enough.
Xiaozhi Wang
doaj  

Implicit Multifunction Theorems in Banach Spaces

Journal of Applied Mathematics, 2014
This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property ...
Ming-ge Yang, Yi-fan Xu
doaj   +1 more source

Approximate Solutions of Variational Inequalities and the Ekeland Principle

Mathematics
Let K be a closed convex subset of a real Banach space X, and let F be a map from X to its dual X*. We study the so-called variational inequality problem: given y∈X*,, does there exist x0∈K such that (in standard notation) F(x0)−y,x−x0≥0 for all x∈K ...
Raffaele Chiappinelli, David E. Edmunds
doaj   +1 more source

Oettli-Théra Theorem and Ekeland Variational Principle in Fuzzy b-Metric Spaces

Axioms
The purpose of this paper is to establish the Oettli–The´ra theorem in the setting of KM-type fuzzy b-metric spaces. To achieve this, we first prove a lemma that removes the constraints on the space coefficients, which significantly simplifies the proof ...
Xuan Liu, Fei He, Ning Lu
doaj   +1 more source