Geodesic
Asymptotic behavior of solutions of nonlinear difference equations
Mathematica Bohemica, Tome 129 (2004) no. 4, pp. 349-359.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2004.134043
Classification : 39A10, 39A11
Keywords: difference equation; asymptotic behavior 
@article{10_21136_MB_2004_134043,
     author = {Migda, Janusz},
     title = {Asymptotic behavior of solutions of nonlinear difference equations},
     journal = {Mathematica Bohemica},
     pages = {349--359},
     publisher = {mathdoc},
     volume = {129},
     number = {4},
     year = {2004},
     doi = {10.21136/MB.2004.134043},
     mrnumber = {2102609},
     zbl = {1080.39501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134043/}
}
TY  - JOUR
AU  - Migda, Janusz
TI  - Asymptotic behavior of solutions of nonlinear difference equations
JO  - Mathematica Bohemica
PY  - 2004
SP  - 349
EP  - 359
VL  - 129
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134043/
DO  - 10.21136/MB.2004.134043
LA  - en
ID  - 10_21136_MB_2004_134043
ER  - 
%0 Journal Article
%A Migda, Janusz
%T Asymptotic behavior of solutions of nonlinear difference equations
%J Mathematica Bohemica
%D 2004
%P 349-359
%V 129
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134043/
%R 10.21136/MB.2004.134043
%G en
%F 10_21136_MB_2004_134043
Migda, Janusz. Asymptotic behavior of solutions of nonlinear difference equations. Mathematica Bohemica, Tome 129 (2004) no. 4, pp. 349-359. doi : 10.21136/MB.2004.134043. http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134043/

Cité par Sources :