Search results for "Difference equation"
showing 10 items of 21 documents
How to control stock markets
1994
This paper provides a different approach to the analysis of imperfect stock markets. The model we are concerned with is described by the interaction of three institutional classes of agents (the specialist trader, the professional trader and the non-professional trader), sharing different information. The dynamical discrete-time system obtained can be changed into a second-order linear difference equation forced by the fundamental value of the specialist trader. Using typical tools of control theory, we study the behaviour of the professional trader’s fundamental value influenced by the specialist’s one. © 1994 Taylor & Francis Group, LLC.
General Solution of a Second-Order Nonhomogenous Linear Difference Equation with Noncommutative Coefficients
2010
The detailed construction of the general solution of a second-order nonhomogenous linear operator-difference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by studying some applications belonging to different mathematical contexts.
Positive solutions of discrete boundary value problems with the (p,q)-Laplacian operator
2017
We consider a discrete Dirichlet boundary value problem of equations with the (p,q)-Laplacian operator in the principal part and prove the existence of at least two positive solutions. The assumptions on the reaction term ensure that the Euler-Lagrange functional, corresponding to the problem, satisfies an abstract two critical points result.
Periodic Solutions of the Second Order Quadratic Rational Difference Equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}} $$ x n + 1 = α ( 1 + x n ) x n…
2016
The aim of this article is to investigate the periodic nature of solutions of a rational difference equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}}. {(*)} $$ We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*). We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter \(\alpha \) and nonnegative initial conditions.
Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition
2021
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.
Elementary symmetric functions of two solvents of a quadratic matrix equations
2008
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.
On optimal estimates for the solutions of linear difference equations on the circle
1976
A linear difference equation arising in the proof of Moser's twist mapping theorem is solved and optimal estimates for the solution are established.
Nonlocal discrete ∞-Poisson and Hamilton Jacobi equations
2015
In this paper we propose an adaptation of the ∞-Poisson equation on weighted graphs, and propose a finer expression of the ∞-Laplace operator with gradient terms on weighted graphs, by making the link with the biased version of the tug-of-war game. By using this formulation, we propose a hybrid ∞-Poisson Hamilton-Jacobi equation, and we show the link between this version of the ∞-Poisson equation and the adaptation of the eikonal equation on weighted graphs. Our motivation is to use this extension to compute distances on any discrete data that can be represented as a weighted graph. Through experiments and illustrations, we show that this formulation can be used in the resolution of many ap…
On the Second Order Rational Difference Equation $$x_{n+1}=\beta +\frac{1}{x_n x_{n-1}}$$ x n + 1 = β + 1 x n x n - 1
2016
The author investigates the local and global stability character, the periodic nature, and the boundedness of solutions of the second-order rational difference equation $$x_{n+1}=\beta +\frac{1}{x_{n}x_{n-1}}, \quad n=0,1,\ldots ,$$ with parameter \(\beta \) and with arbitrary initial conditions such that the denominator is always positive. The main goal of the paper is to confirm Conjecture 8.1 and to solve Open Problem 8.2 stated by A.M. Amleh, E. Camouzis and G. Ladas in On the Dynamics of a Rational Difference Equations I (International Journal of Difference Equations, Volume 3, Number 1, 2008, pp.1–35).
Modeling Political Corruption in Spain
2021
Political corruption is a universal phenomenon. Even though it is a cross-country reality, its level of intensity and the manner of its effect vary worldwide. In Spain, the demonstrated political corruption cases that have been echoed by the media in recent years for their economic, judicial and social significance are merely the tip of the iceberg as regards a problem hidden by many interested parties, plus the shortage of the means to fight against it. This study models and quantifies the population at risk of committing political corruption in Spain by identifying and quantifying the drivers that explain political corruption. Having quantified the problem, the model allows changes to be …