Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term
Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 639-647

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

MR Zbl
In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation \[ \Delta (x_{n}-p_{n} x_{\tau (n)})+f(n,x_{\sigma (n)})=q_{n} \] are obtained. Examples are included to illustrate the results.
In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation \[ \Delta (x_{n}-p_{n} x_{\tau (n)})+f(n,x_{\sigma (n)})=q_{n} \] are obtained. Examples are included to illustrate the results.
DOI : 10.21136/MB.2001.134192
Classification : 39A10, 39A11
Keywords: difference equations; nonlinear; forced term; nonoscillation
Zhang, B. G.; Sun, Y. J. Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term. Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 639-647. doi: 10.21136/MB.2001.134192
@article{10_21136_MB_2001_134192,
     author = {Zhang, B. G. and Sun, Y. J.},
     title = {Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term},
     journal = {Mathematica Bohemica},
     pages = {639--647},
     year = {2001},
     volume = {126},
     number = {3},
     doi = {10.21136/MB.2001.134192},
     mrnumber = {1970266},
     zbl = {0982.39003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134192/}
}
TY  - JOUR
AU  - Zhang, B. G.
AU  - Sun, Y. J.
TI  - Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term
JO  - Mathematica Bohemica
PY  - 2001
SP  - 639
EP  - 647
VL  - 126
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134192/
DO  - 10.21136/MB.2001.134192
LA  - en
ID  - 10_21136_MB_2001_134192
ER  - 
%0 Journal Article
%A Zhang, B. G.
%A Sun, Y. J.
%T Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term
%J Mathematica Bohemica
%D 2001
%P 639-647
%V 126
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134192/
%R 10.21136/MB.2001.134192
%G en
%F 10_21136_MB_2001_134192

[1] R. P. Agarwal: Difference Equations and Inequalities. Marcel Dekker, New York, 2000. | MR | Zbl

[2] R. P. Agarwal, P. J. Y. Wong: Advanced Topics in Difference Equations. Kluwer, Dordrecht, 1997. | MR

[3] M. P. Chen, B. G. Zhang: The existence of the bounded positive solutions of delay difference equations. PanAmerican Math. J. 3 (1993), 79–94. | MR

[4] J. R. Graef, A. Miciano, P. W. Spikes, P. Sundaram, E. Thandapani: On the asymptotic behavior of solutions of a nonlinear difference equation. Proceedings of the First International Conference on Difference Equations, Gordan and Breach, New York, 1995, pp. 223–229. | MR

[5] J. R. Graef, A. Miciano, P. W. Spikes, P. Sundaram, E. Thandapani: Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations. J. Austral. Math. Soc. Ser. B 38 (1996), 163–171. | DOI | MR

[6] J. R. Graef, P. W. Spikes: Boundedness and asymptotic behavior of solutions of a forced difference equations. Internat. J. Math. and Math. Sci. 17 (1994), 397–400. | DOI | MR

[7] J. R. Graef, J. Jaros, A. Miciano, P. W. Spikes: Oscillation and nonoscillation results for nonlinear difference equations with a forcing term. Proceedings of the first International Conference on Difference Equations, Gordan and Breach, New York, 1995, pp. 213–222. | MR

[8] B. G. Zhang, H. Wang: The existence of nonoscillatory and oscillatory solutions of neutral difference equations. Dynam. Systems Appl. 6 (1997), 411–428. | MR

[9] B. S. Lalli, B. G. Zhang: On existence of positive solutions and bounded oscillations for neutral difference equations. J. Math. Anal. Appl. 166 (1992), 272–287. | DOI | MR

[10] B. S. Lalli, B. G. Zhang, J. Z. Li: On the oscillation of solutions and existence of positive solutions of neutral difference equations. J. Math. Anal. Appl. 158 (1991), 213–233. | DOI | MR

[11] E. Thandapani, J. R. Graef, P. W. Spikes: On existence of positive solutions and oscillations of neutral difference equations of odd order. J. Differ. Equations Appl. 2 (1996), 175–183. | DOI | MR

[12] Wudu Lu: Existence of nonoscillatory solutions of first order nonlinear neutral equations. J. Austral. Math. Soc. Ser. B 32 (1990), 180–192. | DOI | Zbl

[13] B. G. Zhang, H. Wang: The existence of nonoscillatory and oscillatory solutions of neutral difference equations. Dynam. Systems Appl. 6 (1997), 411–428. | MR

Cité par Sources :