# Asymptotic behavior of solutions of nonlinear difference equations

Mathematica Bohemica (2004)

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

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topMigda, 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 -

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