# Existence criteria for positive solutions of a nonlinear difference inequality

Annales Polonici Mathematici (2000)

- Volume: 73, Issue: 3, page 197-220
- ISSN: 0066-2216

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topCheng, Sui, and Zhang, Guang. "Existence criteria for positive solutions of a nonlinear difference inequality." Annales Polonici Mathematici 73.3 (2000): 197-220. <http://eudml.org/doc/262826>.

@article{Cheng2000,

abstract = {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.},

author = {Cheng, Sui, Zhang, Guang},

journal = {Annales Polonici Mathematici},

keywords = {Sturm type comparison theorem; limit comparison theorem; nth order linear difference equation; eventually positive solution; eventually positive nonincreasing solution; neutral difference equation; nonlinear delay difference inequality; nonlinear difference inequalities; Riccati type transformation; positive solutions; nonincreasing solutions; comparison theorems},

language = {eng},

number = {3},

pages = {197-220},

title = {Existence criteria for positive solutions of a nonlinear difference inequality},

url = {http://eudml.org/doc/262826},

volume = {73},

year = {2000},

}

TY - JOUR

AU - Cheng, Sui

AU - Zhang, Guang

TI - Existence criteria for positive solutions of a nonlinear difference inequality

JO - Annales Polonici Mathematici

PY - 2000

VL - 73

IS - 3

SP - 197

EP - 220

AB - 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.

LA - eng

KW - Sturm type comparison theorem; limit comparison theorem; nth order linear difference equation; eventually positive solution; eventually positive nonincreasing solution; neutral difference equation; nonlinear delay difference inequality; nonlinear difference inequalities; Riccati type transformation; positive solutions; nonincreasing solutions; comparison theorems

UR - http://eudml.org/doc/262826

ER -

## References

top- [1] R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992. Zbl0925.39001
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- [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. Zbl0732.39002
- [6] J. Popenda, The oscillation of solutions of difference equations, Comput. Math. Appl. 28 (1994), 271-279. Zbl0807.39006
- [7] J. Yan, Oscillation of solutions of first order delay differential equations, Nonlinear Anal. 11 (1987), 1279-1287. Zbl0639.34067
- [8] J. Yan and C. Qian, Oscillation and comparison results for delay difference equations, J. Math. Anal. Appl. 165 (1992), 346-360. Zbl0818.39002
- [9] J. S. Yu, A note on 'Oscillation of solutions of first order delay differential equations', J. Math. Res. Exposition 10 (1990), 290-293. Zbl0772.34052
- [10] B. G. Zhang and S. S. Cheng, Oscillation criteria and comparison theorems for delay difference equations, Fasc. Math. 25 (1995), 13-32. Zbl0830.39005

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