Results 61 to 70 of about 179 (120)

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
openaire   +3 more sources

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
doaj  

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.
openaire   +2 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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.
openaire   +3 more sources

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
doaj   +1 more source

Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Boundary Value Problems, 2006
The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN. The solutions will be obtained in a subspace of the Sobolev space W1/p(RN).
Mihai Mihăilescu
doaj   +1 more source

Maximum principle for a nonlinear size-structured model of fish and fry management

Nonlinear Analysis, 2018
This paper investigates the maximum principle for a nonlinear size-structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry.
Rong Liu, Guirong Liu
doaj   +1 more source