2008/12/17 by Orlando Merino, Merino, Orlando
Computer Science · Mathematics · #39A11 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Analysis #Polynomial and algebraic computation #advanced mathematical theories #math.DS #msc:39A11
paper · pdf · doi:10.48550/arxiv.0812.3398
10 pages
arxiv created 2008/12/17 · openalex publication_date 2008/12/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p and q be arbitrary positive numbers. It is shown that if q < p, then all solutions to the difference equation xn+1 = \fracp+q xn1+xn-1, n=0,1,2,..., x-1>0, x0>0 converge to the positive equilibrium x = 1/2(q-1 + √((q-1)2 + 4 p)). \medskip The above result, taken together with the 1993 result of Kocić and Ladas for equation (E) with q ≥ p, gives global attractivity of the positive equilibrium of (E) for all positive values of the parameters, thus completing the proof of a conjecture of Ladas.