Yang, Xiaofan Global asymptotic stability in a class of generalized Putnam equations. (English) Zbl 1104.39012 J. Math. Anal. Appl. 322, No. 2, 693-698 (2006). The author proves that for every \(m\geq 3\) there is a unique equilibrium point that attracts globally all other solutions to the so-called “generalized Putnam equations” of the form \[ x_{n+1}= \left(\sum_{i=0}^{m-2} x_{n-i} + x_{n-m+1}x_{n-m})/(x_nx_{n-1} + \sum_{i=2}^mx_{n-i}\right), \] where \(n=0,1,2,\dots\). Reviewer: Nguyen Van Minh (Carrollton) Cited in 11 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations Keywords:rational difference equation; equilibrium; global asymptotic stability; generalized Putnam equation PDFBibTeX XMLCite \textit{X. Yang}, J. Math. Anal. Appl. 322, No. 2, 693--698 (2006; Zbl 1104.39012) Full Text: DOI References: [1] Amleh, A. M.; Kruse, N.; Ladas, G., On a class of difference equations with strong negative feedback, J. Difference Equations Appl., 5, 497-515 (1999) · Zbl 0951.39002 [2] Kocic, V. L.; Ladas, G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (1993), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0787.39001 [3] Kruse, N.; Nesemann, T., Global asymptotic stability in some discrete dynamic systems, J. Math. Anal. Appl., 235, 151-158 (1999) · Zbl 0933.37016 [4] Ladas, G., Open problems and conjectures, J. Differ. Equations Appl., 4, 497-499 (1998) [5] Li, X.; Zhu, D., Global asymptotic stability in a rational equation, J. Differ. Equations Appl., 9, 833-839 (2003) · Zbl 1055.39014 [6] Li, X.; Zhu, D., Global asymptotic stability for two recursive difference equations, Appl. Math. Comput., 150, 481-492 (2004) · Zbl 1044.39006 [7] Nesemann, T., Positive nonlinear difference equations: some results and applications, Nonlinear Anal., 47, 4704-4717 (2001) · Zbl 1042.39510 [8] Papaschinopoulos, G.; Schinas, C. J., Global asymptotic stability and oscillation of a family of difference equations, J. Math. Anal. Appl., 294, 614-620 (2004) · Zbl 1055.39017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.