On positive solutions of a imageth order difference equation Original Research Article

In this work we show that the following difference equation: View the MathML sourcexn+1=xn−k1+xn+⋯+xn−k+1,n=0,1,…, Turn MathJax on where k∈Nk∈N is fixed, has a positive solution which converges to zero. This result solves Open Problem 11.4.10 (a) in [M.R.S. Kulenović, G. Ladas, Dynamics of Second Order Rational Difference Equations. With Open Problems and Conjectures, Chapman and Hall/CRC, 2001].