On the recursive sequence Xn+1 = B + xn-k/ α0xn+...+αk-1X n-k+1+γ

Abstract

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation in the title is investigated, where all the coefficients are nonnegative real numbers. The paper is motivated by an open problem proposed by Ladas [Open problems and conjectures, J. Differ. Equations Appl., 5 (1999), 211-215].