On the difference equation x n+1 = a+bx n-k-cx n-m/1+g(x n-1)

Abstract

In this paper we consider the difference equation x n+1 = a+bx n-k-cx n-m/1+g(x n-1) where a, b, c are nonegative real numbers, k, l, m are nonnegative integers and g(x) is a nonnegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation.