Asymptotic behavior of solutions of nonlinear difference equations

Janusz Migda

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 4, page 349-359
  • ISSN: 0862-7959

Abstract

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The nonlinear difference equation x n + 1 - x n = a n ϕ n ( x σ ( n ) ) + b n , ( E ) where ( a n ) , ( b n ) are real sequences, ϕ n ℝ ⟶ ℝ , ( σ ( n ) ) is a sequence of integers and lim n ⟶ ∞ σ ( n ) = ∞ , is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation y n + 1 - y n = b n are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained.

How to cite

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Migda, Janusz. "Asymptotic behavior of solutions of nonlinear difference equations." Mathematica Bohemica 129.4 (2004): 349-359. <http://eudml.org/doc/249394>.

@article{Migda2004,
abstract = {The nonlinear difference equation \[ x\_\{n+1\}-x\_n=a\_n\varphi \_n(x\_\{\sigma (n)\})+b\_n, \qquad \mathrm \{(\text\{E\})\}\] where $(a_n), (b_n)$ are real sequences, $\varphi _n\: \mathbb \{R\}\longrightarrow \mathbb \{R\}$, $(\sigma (n))$ is a sequence of integers and $\lim _\{n\longrightarrow \infty \}\sigma (n)=\infty $, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation $y_\{n+1\}-y_n=b_n$ are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained.},
author = {Migda, Janusz},
journal = {Mathematica Bohemica},
keywords = {difference equation; asymptotic behavior; difference equation; asymptotic behavior},
language = {eng},
number = {4},
pages = {349-359},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic behavior of solutions of nonlinear difference equations},
url = {http://eudml.org/doc/249394},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Migda, Janusz
TI - Asymptotic behavior of solutions of nonlinear difference equations
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 4
SP - 349
EP - 359
AB - The nonlinear difference equation \[ x_{n+1}-x_n=a_n\varphi _n(x_{\sigma (n)})+b_n, \qquad \mathrm {(\text{E})}\] where $(a_n), (b_n)$ are real sequences, $\varphi _n\: \mathbb {R}\longrightarrow \mathbb {R}$, $(\sigma (n))$ is a sequence of integers and $\lim _{n\longrightarrow \infty }\sigma (n)=\infty $, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation $y_{n+1}-y_n=b_n$ are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained.
LA - eng
KW - difference equation; asymptotic behavior; difference equation; asymptotic behavior
UR - http://eudml.org/doc/249394
ER -

References

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