| Автор | Berenhaut, Kenneth S. |
| Автор | Jones, Austin H. |
| Дата выпуска | 2012 |
| dc.description | This paper studies the behaviour of positive solutions of the recursive equation , , where is the mth elementary symmetric polynomial on k variables, for , and , with . A variant of Newton's inequalities is employed. Included among the results is a generalization of a particular case of Theorem 4.11 in E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman & Hall/CRC Press, Boca Raton, 2004. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | difference equations |
| Тема | asymptotic behaviour |
| Тема | symmetric functions |
| Тема | elementary symmetric polynomials |
| Тема | Newton's inequalities |
| Тема | periodicity |
| Тема | 39A10 |
| Тема | 39A11 |
| Название | Asymptotic behaviour of solutions to difference equations involving ratios of elementary symmetric polynomials |
| Тип | research-article |
| DOI | 10.1080/10236198.2010.535526 |
| Electronic ISSN | 1563-5120 |
| Print ISSN | 1023-6198 |
| Журнал | Journal of Difference Equations and Applications |
| Том | 18 |
| Первая страница | 963 |
| Последняя страница | 972 |
| Аффилиация | Berenhaut, Kenneth S.; Department of Mathematics, Wake Forest University |
| Аффилиация | Jones, Austin H.; Department of Mathematics, Wake Forest University |
| Выпуск | 6 |
| Библиографическая ссылка | Berenhaut, K.S. and Guy, R.T. 2009. Symmetric functions and difference equations with asymptotically period-two solutions. Int. J. Differ. Equ., 4(1): 43–48. |
| Библиографическая ссылка | Berenhaut, K.S. and Stevic, S. 2007. The global attractivity of a higher order rational difference equation. J. Math. Anal. Appl., 326(2): 940–944. |
| Библиографическая ссылка | Berenhaut, K.S., Foley, J.D. and Stevic, S. 2007. The global attractivity of the rational difference equation . Appl. Math. Lett., 20: 54–58. |
| Библиографическая ссылка | Berenhaut, K.S., Guy, R.T. and Barrett, C.J. 2010. Global asymptotic stability for minimum-delay difference equations. J. Differ. Equ. Appl., in press |
| Библиографическая ссылка | Billingsley, P. 1995. Probability and Measure, 3rd ed., New York: Wiley. |
| Библиографическая ссылка | Devault, R., Ladas, G. and Schultz, S.W. 1998. On the recursive sequence . Proc. Am. Math. Soc., 126(11): 3257–3261. |
| Библиографическая ссылка | El-Mikkawy, M. and Sogabe, T. 2010. Notes on particular symmetric polynomials with applications. Appl. Math. Comput., 215(9): 3311–3317. |
| Библиографическая ссылка | El-Metwally, H., Grove, E.A. and Ladas, G. 2000. A global convergence result with applications to periodic solutions. J. Math. Anal. Appl., 245(1): 161–170. |
| Библиографическая ссылка | El-Metwally, H., Grove, E.A., Ladas, G. and Voulov, H.D. 2001. On the global attractivity and the periodic character of some difference equations. On the occasion of the 60th birthday of Calvin Ahlbrandt. J. Differ. Equ. Appl., 7(6): 837–850. |
| Библиографическая ссылка | Grove, E.A. and Ladas, G. 2004. Periodicities in Nonlinear Difference Equations, Boca Raton, FL: Chapman & Hall/CRC Press. |
| Библиографическая ссылка | Ladas, G. 1998. Open problems and conjectures. J. Differ. Equ. Appl., 4(3): 311–313. |
| Библиографическая ссылка | Macdonald, I.G. 1995. Symmetric Functions and Hall Polynomials, 2nd ed., With contributions by A. Zelevinsky, Oxford Mathematical Monographs, Oxford Science Publications New York: The Clarendon Press, Oxford University Press. |
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| Библиографическая ссылка | Pollard, H. and Diamond, H.G. 1975. The theory of algebraic numbers, 2nd ed., Carus Mathematical Monographs, Number 9 Washington, DC: Mathematical Association of America. |
| Библиографическая ссылка | Stewart, I. 2004. Galois Theory, 3rd ed., Chapman & Hall/CRC Mathematics Boca Raton, FL: Chapman & Hall/CRC. |
| Библиографическая ссылка | Sun, T. and Xi, H. 2008. The periodic character of the difference equation . Adv. Differ. Equ., 2008 Article ID 143723, 6 pp |
