This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.
@article{bwmeta1.element.bwnjournal-article-apmv73z3p197bwm,
author = {Cheng, Sui and Zhang, Guang},
title = {Existence criteria for positive solutions of a nonlinear difference inequality},
journal = {Annales Polonici Mathematici},
volume = {75},
year = {2000},
pages = {197-220},
zbl = {0974.39001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv73z3p197bwm}
}
Cheng, Sui; Zhang, Guang. Existence criteria for positive solutions of a nonlinear difference inequality. Annales Polonici Mathematici, Tome 75 (2000) pp. 197-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv73z3p197bwm/
[000] [1] R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992. | Zbl 0925.39001
[001] [2] I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, Clarendon Press, Oxford, 1991. | Zbl 0780.34048
[002] [3] I. Györi and M. Pituk, Asymptotic formulae for the solutions of a linear delay difference equation, J. Math. Anal. Appl. 195 (1995), 376-392. | Zbl 0846.39003
[003] [4] B. S. Lalli, Oscillation theorems for neutral difference equations, Comput. Math. Appl. 28 (1994), 191-202. | Zbl 0807.39004
[004] [5] B. S. Lalli, B. G. Zhang and 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. | Zbl 0732.39002
[005] [6] J. Popenda, The oscillation of solutions of difference equations, Comput. Math. Appl. 28 (1994), 271-279. | Zbl 0807.39006
[006] [7] J. Yan, Oscillation of solutions of first order delay differential equations, Nonlinear Anal. 11 (1987), 1279-1287. | Zbl 0639.34067
[007] [8] J. Yan and C. Qian, Oscillation and comparison results for delay difference equations, J. Math. Anal. Appl. 165 (1992), 346-360. | Zbl 0818.39002
[008] [9] J. S. Yu, A note on 'Oscillation of solutions of first order delay differential equations', J. Math. Res. Exposition 10 (1990), 290-293. | Zbl 0772.34052
[009] [10] B. G. Zhang and S. S. Cheng, Oscillation criteria and comparison theorems for delay difference equations, Fasc. Math. 25 (1995), 13-32. | Zbl 0830.39005