ON DYNAMICS OF SOME DIFFERENCE EQUATIONS

Authors

  • Akhtam Dzhalilov Turin Polytechnic University in Tashkent
  • Mukhriddin Kakhkhorov Jizzakh State Pedagogical Institute

Keywords:

difference equation, power series, solution of difference equation, asymptotic behaviour

Abstract

In present work we investigate the difference equations $x_{n+1}=f(x_{n}),\,\,n\geq0.$
We consider the case when the function $f$ is power series. It is proved that under some condition to $f$
the solution of difference equation asymptotically equivalent to $bn^{\alpha},\,\alpha>0,$ as $n\rightarrow \infty.$

References

Lothar Berg., Asymptotische Einschliebung von Losungenexpliziter Operatordifferentialgleichungen.MathematischeNachrichten.V. 56, Issue 1-6, p. 1969-173. (1973)

Kolmogorov A. N., Fomin S.V. Introductory Real Analysis.Dover Publications. INC, New York (1975)

Cushing, J., and S. Henson, Global dynamics of some peri-odically forced, monotone difference equations, J. DifferenceEqu. Appl. 7(6), 859-872, (2001)

Cushing, J., Cycle chains and the LPA model, J. DifferenceEqu. Appl. 9, 655-670. (2003)

Saber Elaydi., An Introduction to Difference Equations. Undergraduate Texts in Mathematics. Springer. (2004)

Published

2021-03-26

How to Cite

Dzhalilov, A., & Kakhkhorov, M. (2021). ON DYNAMICS OF SOME DIFFERENCE EQUATIONS. Acta of Turin Polytechnic University in Tashkent, 11(1), 27–28. Retrieved from https://acta.polito.uz/index.php/journal/article/view/dzhalilov