Abstract

The subject of the paper are two types of rational difference equations of the form xn+1=f(xn,xn−1,xn−2,xn−3)+g(xn,xn−1,xn−2,xn−3)xm+1n−3+af(xn,xn−1,xn−2,xn−3)+g(xn,xn−1,xn−2,xn−3)xmn−3+a and xn+1=A1xnxn−1+A2xn−1xn−2+⋯+Ak−1xn−k+2xn−k+1−1x2n−k. with suitable functions f,g and constants m,a,k,A1,…,An−1. The two central results deal with existence and stability of equilibrium solutions.