An example of nonlinear $q$-difference equation

BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR DIFFERENCE EQUATION

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

POSITIVE SOLUTIONS OF q-DIFFERENCE EQUATION

In this paper we investigate the existence of positive solutions of the q-difference equation −D2 qu(t) = a(t) f(u(t)) with some boundary conditions by applying a fixed point theorem in cones. 1. Preliminaries In many of the mathematical models in science such as models of chemical problems, population or concentration in biology, and many problems in physics and economics, we need to investiga...

The Beverton–Holt q-difference equation

The Beverton-Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton-Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of period...

Existence of positive solutions of nonlinear fractional q-difference equation with parameter

*Correspondence: [email protected] School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P.R. China Abstract In this paper, we study the boundary value problem of a class of nonlinear fractional q-difference equations with parameter involving the Riemann-Liouville fractional derivative. By means of a fixed point theorem in cones, some positive solutions are obtained. As...

A Nonlinear Differential-difference Equation of Growth.