A complex number q with 0 < |q| < 1 is fixed. By an analytic q-difference equation we mean an equation which can be represented by a matrix equation Y (z) = A(z)Y (qz) where A(z) is an invertible n× n-matrix with coefficients in the field K = C({z}) of the convergent Laurent series and where Y (z) is a vector of size n. The aim of this paper is to give an overview of our present knowledge of th...

Asymptotic properties of some non-linear difference equations are considered. AMS(1980) Subject Classification: 39A12, 45E99..

We shall develop here a galois theory for difference equations. In the PicardVessiot galois theory for differential equations, the basic objects of study are the Picard-Vessiot extension of a field and its associated galois group. Recall that a Picard-Vessiot extension of a differential field k is an extension K generated by a fundamental set of solutions of a linear differential equation and h...

Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...

This paper is on the solutions of fuzzy initial value problems for fourth-order fuzzy differential equations with positive and negative fuzzy coefficients by fuzzy Laplace transform. Examples are solved. Conclusions are given.

in this paper, we propose the least-squares method for computing the positive solution of a m  n fully fuzzy linear system (ffls) of equations, where m > n, based on kaman&apos;s arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coecient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the n...