Classifications and existence of positive solutions of a higher order nonlinear difference equation

Wan-Tong Li; Sui Cheng

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 1, page 137-153
  • ISSN: 0010-1354

Abstract

top
A classification scheme for the eventually positive solutions of a class of higher order nonlinear difference equations is given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of such solutions are provided.

How to cite

top

Li, Wan-Tong, and Cheng, Sui. "Classifications and existence of positive solutions of a higher order nonlinear difference equation." Colloquium Mathematicae 83.1 (2000): 137-153. <http://eudml.org/doc/210768>.

@article{Li2000,
abstract = {A classification scheme for the eventually positive solutions of a class of higher order nonlinear difference equations is given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of such solutions are provided.},
author = {Li, Wan-Tong, Cheng, Sui},
journal = {Colloquium Mathematicae},
keywords = {sublinear function; nonlinear difference equation; superlinear function; eventually positive solution; existence theorem; positive solutions; higher-order nonlinear difference equation; asymptotic},
language = {eng},
number = {1},
pages = {137-153},
title = {Classifications and existence of positive solutions of a higher order nonlinear difference equation},
url = {http://eudml.org/doc/210768},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Li, Wan-Tong
AU - Cheng, Sui
TI - Classifications and existence of positive solutions of a higher order nonlinear difference equation
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 137
EP - 153
AB - A classification scheme for the eventually positive solutions of a class of higher order nonlinear difference equations is given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of such solutions are provided.
LA - eng
KW - sublinear function; nonlinear difference equation; superlinear function; eventually positive solution; existence theorem; positive solutions; higher-order nonlinear difference equation; asymptotic
UR - http://eudml.org/doc/210768
ER -

References

top
  1. [1] R. P. Agarwal, Difference Equations and Inequalities, Academic Press, New York, 1992. Zbl0925.39001
  2. [2] M. P. Chen and B. G. Zhang, The existence of bounded positive solutions of delay difference equations, PanAmerican Math. J. 3 (1993), 79-94. Zbl0847.39005
  3. [3] S. S. Cheng, H. J. Li and W. T. Patula, Bounded and zero convergent solutions of second order difference equations, J. Math. Anal. Appl. 141 (1989), 463-483. Zbl0698.39002
  4. [4] S. S. Cheng and W. T. Patula, An existence theorem for a nonlinear difference equation, Nonlinear Anal. 20 (1993), 193-203. Zbl0774.39001
  5. [5] I. Győri and G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Math. Monographs, Clarendon Press, 1991. Zbl0780.34048
  6. [6] X. Z. He, Oscillatory and asymptotic behaviour of second order nonlinear difference equations, J. Math. Anal. Appl. 175 (1993), 482-498. Zbl0780.39001
  7. [7] J. W. Hooker and W. T. Patula, Riccati type transformations for second order linear difference equations, J. Math. Anal. Appl. 82 (1981), 451-462. Zbl0471.39007
  8. [8] J. W. Hooker and W. T. Patula, A second order nonlinear difference equation: Oscillation and asymptotic behavior, ibid. 91 (1983), 9-29. Zbl0508.39005
  9. [9] B. Szmanda, Characterization of oscillation of second order nonlinear difference equations, Bull. Polish Acad. Sci. Math. 34 (1986), 133-141. Zbl0598.39004
  10. [10] X. B. Wu, Some notes on ``Oscillatory and asymptotic behavior of second order nonlinear difference equations'', J. Math. Anal. Appl. 189 (1995), 310-312. Zbl0816.39001
  11. [11] A. Zafer and R. S. Dahiya, Oscillation of a neutral difference equation, Appl. Math. Lett. 6 (1993), 71-74. Zbl0772.39001
  12. [12] X. L. Zhou and J. R. Yan, Oscillation property of higher order difference equations, Comput. Math. Appl. 31 (1996), no. 12, 61-68. Zbl0855.39016
  13. [13] X. L. Zhou and J. R. Yan, Oscillation of higher order difference equations, Chinese Ann. Math. 15A (1994), 692-700. Zbl0815.39004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.