scholarly journals Existence of General Competitive Equilibria: A Variational Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
G. Anello ◽  
F. Rania
Keyword(s):  
Variational Inequalities ◽  
Finite Number ◽  
Variational Methods ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Utility Functions ◽  
Locally Lipschitz ◽  
Competitive Equilibria

We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities.

scholarly journals Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
I. Benedetti ◽  
M. B. Donato ◽  
M. Milasi
Keyword(s):  
Variational Inequality ◽  
Equilibrium Model ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Quasivariational Inequalities ◽  
Existence Of Equilibrium ◽  
Upper Semicontinuous ◽  
Generalized Quasivariational Inequalities ◽  
Quasi Variational Inequality

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach.

scholarly journals Multiple positive solutions for nonlocal elliptic problems involving the Hardy potential and concave–convex nonlinearities

2020 ◽  
pp. 2050008
Author(s):  
Shaya Shakerian
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variational Approach ◽  
Nehari Manifold ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].

scholarly journals Antiperiodic Solutions forp-Laplacian Systems via Variational Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lifang Niu ◽  
Kaimin Teng
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Variational Approach ◽  
Existence Of Solutions

We establish the existence of solutions forp-Laplacian systems with antiperiodic boundary conditions through using variational methods.

scholarly journals Maxwell quasi-variational inequalities in superconductivity

2021 ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Variational Inequalities ◽  
Magnetic Field Dependence ◽  
Existence Result ◽  
Time Discretization ◽  
Stability And Convergence ◽  
Well Posedness ◽  
Modeling And Analysis ◽  
Quasi Variational Inequality ◽  
The Stability ◽  
Point Argument

This paper is devoted to the mathematical modeling and analysis of a hyperbolic Maxwell quasi-variational inequality (QVI) for  the Bean-Kim superconductivity model with temperature and magnetic field dependence in the critical current. Emerging from the Euler time discretization, we analyze the corresponding H(curl)-elliptic QVI and prove its existence using a fixed-point argument in combination with techniques from variational inequalities and Maxwell's equations.  Based on the existence result  for the H(curl)-elliptic QVI, we examine the  stability and convergence of the Euler scheme, which serve as our fundament for the well-posedness of the governing hyperbolic Maxwell QVI.

scholarly journals Hyperbolic Maxwell variational inequalities of the second kind

2020 ◽  
Vol 26 ◽  
pp. 34 ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Variational Inequalities ◽  
Existence Result ◽  
Semigroup Theory ◽  
Regularity Property ◽  
Well Posedness ◽  
Test Functions ◽  
Local Boundedness ◽  
Subdifferential Calculus ◽  
Faraday’S Law ◽  
Yosida Regularization

We analyze a class of hyperbolic Maxwell variational inequalities of the second kind. By means of a local boundedness assumption on the subdifferential of the underlying nonlinearity, we prove a well-posedness result, where the main tools for the proof are the semigroup theory for Maxwell’s equations, the Yosida regularization and the subdifferential calculus. The second part of the paper focuses on a more general case omitting the local boundedness assumption. In this case, taking into account more regular initial data and test functions, we are able to prove a weaker existence result through the use of the minimal section operator associated with the Nemytskii operator of the governing subdifferential. Eventually, we transfer the developed well-posedness results to the case involving Faraday’s law, which in particular allows us to improve the regularity property of the electric field in the weak existence result.

Stability and Generalized Competitive Equilibria in a Many-to-Many Gale-Shapley Market Model

2016 ◽  
Vol 63 (3) ◽  
pp. 237-254
Author(s):  
Zbigniew Świtalski
Keyword(s):  
Competitive Equilibrium ◽  
College Admissions ◽  
Supply And Demand ◽  
Type A ◽  
Market Model ◽  
Stable Matchings ◽  
Competitive Equilibria

We define, for some variant of a many-to-many market model of Gale-Shapley type, a concept of generalized competitive equilibrium and show that, under suitable conditions, stable matchings in such a model can be represented as competitive equilibria allocations (and vice versa). Our results are far-reaching generalizations of the “discrete supply and demand lemma” of Azevedo, Leshno (2011) for the college admissions market.Using the results of Alkan, Gale (2003), we also prove a theorem on existence of generalized equilibria in our model.

scholarly journals Variational Approach to Quasi-Periodic Solution of Nonautonomous Second-Order Hamiltonian Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Juhong Kuang
Keyword(s):  
Periodic Solution ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Variational Approach ◽  
Second Order ◽  
New Approach ◽  
Second Order Hamiltonian Systems

We deal with the quasi-periodic solutions of the following second-order Hamiltonian systemsx¨(t)=∇F(t,x(t)), wherex(t)=(x1(t),…,xN(t)), and we present a new approach via variational methods and Minmax method to obtain the existence of quasi-periodic solutions to the above equation.

Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions

2015 ◽  
Vol 32 (2) ◽  
pp. 373-410 ◽  
Author(s):  
Yoshiko T. Ikebe ◽  
Yosuke Sekiguchi ◽  
Akiyoshi Shioura ◽  
Akihisa Tamura
Keyword(s):  
Utility Functions ◽  
Competitive Equilibria ◽  
Trading Networks

Competitive equilibrium in two sided matching markets with general utility functions

2011 ◽  
Vol 10 (2) ◽  
pp. 34-36 ◽  
Author(s):  
Saeed Alaei ◽  
Kamal Jain ◽  
Azarakhsh Malekian
Keyword(s):  
Competitive Equilibrium ◽  
Utility Functions ◽  
Matching Markets ◽  
General Utility

scholarly journals Existence and stability of static shells for the Vlasov–Poisson system with a fixed central point mass

2009 ◽  
Vol 146 (2) ◽  
pp. 489-511
Author(s):  
ACHIM SCHULZE
Keyword(s):  
Black Hole ◽  
Simple Model ◽  
Variational Approach ◽  
Existence Result ◽  
Stationary Solutions ◽  
Point Mass ◽  
Classical Solutions ◽  
Poisson System ◽  
Existence And Stability ◽  
Global Existence Result

AbstractWe consider the Vlasov–Poisson system with spherical symmetry and an exterior potential which is induced by a point mass in the center. This system can be used as a simple model for a newtonian galaxy surrounding a black hole. For this system, we establish a global existence result for classical solutions with shell-like initial data, i.e. the support of the density is bounded away from the point mass singularity. We also prove existence and stability of stationary solutions which describe static shells, where we use a variational approach which was established by Y. Guo and G. Rein.

Sign in / Sign up

Export Citation Format

Share Document