ON THE ASYMPTOTICS OF A CLASS OF NONLINEAR DIFFERENCE EQUATIONS

  • Tran Hong Thai Hung Yen University of Technology and Education
Keywords: Difference equations, Asymptotics behavior

Abstract

The asymptotic form of solution is a specific solution of difference equations. It represents the rate of convergence of solution to equilibrium point of difference equations. In this paper, we investigate asymptotic form of a class of nonlinear difference equations. By asymptotic method, we show the existence of a solution of a class of difference equations converging to zero as n " 3, and to determine its asymptotic behavior

References

L. Berg, Asymptotische Darstellungen und Entwicklungen, Dt. Verlag Wiss, Berlin, 1968.

L. Berg, On the asymptotics of nonlinear difference equations, Zeitschrift for Analysis and Ihre Anwendungen, 21, 1061-1074, 2002.

L. Berg, Inclusion theorems for non-linear difference equations with applications, J. Difference Equ. Appl., 10(4), 399-408, 2004.

L. Berg, Corrections to “Inclusion theorems for non-linear difference equations with applications”, J. Difference Equ. Appl., 11(2), 181-182, 2005.

L. Berg, On the asymptotics of the difference equation xn-3 = xn ^1 + xn-1xn-2h , J. Difference Equ. Appl., 14(1), 105-108, 2008.

L. Berg, S. Stevi’c, On the asymptotics of the difference equation yn-k = yn (1 + yn-1…yn-k+1) , J. Difference Equ. Appl., 17(4), 577-586, 2011.

C. H. Gibbons, M. R. S. Kulenovi’c, G. Ladas, On the recursive sequence x x,Math. Sci. Res. Hot-Line, 4(2), 1-11, 2000.

L. Gutnik, S. Stevi’c, On the behaviour of the solutions of a second-order difference equation, Discrete Dyn. Nat. Soc., Art. ID 27562, 14 pages, 2007.

S. Stevi’c, On the recursive sequence ( )- Taiwanese J. Math., 6(3), 405-414, 2002.

S. Stevi’c, On monotone solutions of some classes of difference equations, Discrete Dyn. Nat. Soc., Art. ID 53890, 9 pages, 2006.

S. Stevi’c, On positive solutions of a (k + 1)th order difference equations, Appl. Math. Letter, 19, 427 - 431, 2006.

S. Stevi’c, Asymptotics of some classes of higher order difference equations, Discrete Dyn. Nat. Soc., Art. ID 56813, 20 pages, 2007.

Published
2020-04-15
How to Cite
Tran Hong Thai. (2020). ON THE ASYMPTOTICS OF A CLASS OF NONLINEAR DIFFERENCE EQUATIONS. UTEHY Journal of Science and Technology, 25, 68-70. Retrieved from http://tapchi.utehy.edu.vn/index.php/jst/article/view/358