A generalization of Poincaré's theorem for recurrence systems

Applicable Analysis

Volumn 85, Issue 4, 2006, Pages 373-381

  Pinto, Manuel ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

AMS Subject Classification: 39A10; Asymptotic behavior; Poincar 's system; Recurrence equations

Indexed keywords

EID: 85014731708     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036810500353750     Document Type: Article

References (14)

1. Castillo, S, and Pinto, M. 2000. Asymptotic formulae for nonlinear functional difference equations. Computers & Mathematics with Applications, 42: 551–559.
2. Coffman, CV. 1964. Asymptotic behavior of solutions of ordinary difference equations. Transactions of American Mathematical Society, 110: 22–51.
3. Farkas, G. 2001. On the asymptotics of solutions of Poincaré difference systems. Journal of Difference Equations and Applications, 7: 183–191.
4. Gelfond, AO. 1971. Calculus on Finite Differences, Delhi, India: Hindustan Publ. Corp.
5. Gemignani, L. 1999. “ On a generalization of Poincaré's theorem for matrix difference equations arising from root-finding problems ”. In Structured Matrices in Mathematics, Computer Science, and Engineering II, 265–278. American Mathematical Society (Vadim Olshevsky Ed.).
6. Maté, A, and Nevai, P. 1990. A generalization of Poincaré's theorem for recurrence equations. Journal of Approximation Theory, 63: 92–97.
7. Perron, O. 1909. Über Einen Satz des Herrn Poincaré. Journal fur die Reine und Angewandte Mathematik, 136: 17–37.
8. Pinto, M. 1994. Discrete dichotomies. Computers & Mathematics with Applications, 28: 259–270.
9. Pinto, M. 2003. Null-solutions of difference systems under vanishing perturbation. Journal of Difference Equations and Applications, 9: 1.13
10. Pituk, M. 1997. Asymptotic behavior of a Poincaré recurrence system. Journal of Approximation Theory, 91: 226–243.
11. Pituk, M. 2002. Asymptotic behavior of a nonhomogeneous linear recurrence system. Journal of Mathematical Analysis and Applications, 267: 626–642.
12. Poincaré, H. 1885. Sur les equations lineaires aux differentieles et aux difference finies. American Journal of Mathematics, 7: 203–258.
13. Trench, W. 1993. Asymptotic behavior of solutions of Poincaré difference equations. Proceedings of the American Mathematical Society, 119: 431–438.
14. Trench, W. 1994. Asymptotic behavior of solutions of Poincaré recurrence systems. Computers & Mathematics with Applications, 28: 317–324.