Search results for " Difference equations"
showing 6 items of 6 documents
Exact treatment of operator difference equations with nonconstant and noncommutative coefficients
2013
We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.
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…
One- and multi-locus multi-allele selection models in a random environment
1979
We deduce conditions for stochastic local stability of general perturbed linear stochastic difference equations widely applicable in population genetics. The findings are adapted to evaluate the stability properties of equilibria in classical one- and multi-locus multi-allele selection models influenced by random temporal variation in selection intensities. As an example of some conclusions and biological interpretations we analyse a special one-locus multi-allele model in more detail.
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.
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.