Uncountably many solutions of a third order nonlinear difference equation with neutral delay
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Authors
Zeqing Liu
- Department of Mathematics, Liaoning Normal University Dalian, Liaoning 116029, People's Republic of China.
Xiaoying Zhang
- Department of Mathematics, Liaoning Normal University Dalian, , ., Liaoning 116029, People's Republic of China.
Jeong Sheok Ume
- Department of Mathematics, Changwon National University, Changwon 641-773, Korea.
Shin Min Kang
- Department of Mathematics and the Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, Korea.
Abstract
In this paper, by using the Schauder fixed point theorem, Krasnoselskii fixed point theorem and some
new techniques, we obtain the existence of uncountably many solutions for a third order nonlinear difference
equation with neutral delay of the form
\[\Delta(a(n; x_{a_{1n}}; x_{a_{2n}};... ; x_{a_{rn}})\Delta^2(x_n + b_nx_{n-\tau})+ \Delta h(n; x_{h_{1n}}; x_{h_{2n}}; ... ; x_{h_{kn}})
+ f(n; x_{f_{1n}}; x_{f_{2n}};... ; x_{f_{kn}})
= c_n, n \geq n_0,\]
The results presented improve and generalize some results in literatures. Seven examples are given to
illustrate the results presented in this paper.
Share and Cite
ISRP Style
Zeqing Liu, Xiaoying Zhang, Jeong Sheok Ume, Shin Min Kang, Uncountably many solutions of a third order nonlinear difference equation with neutral delay, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4329--4354
AMA Style
Liu Zeqing, Zhang Xiaoying, Ume Jeong Sheok, Kang Shin Min, Uncountably many solutions of a third order nonlinear difference equation with neutral delay. J. Nonlinear Sci. Appl. (2016); 9(6):4329--4354
Chicago/Turabian Style
Liu, Zeqing, Zhang, Xiaoying, Ume, Jeong Sheok, Kang, Shin Min. "Uncountably many solutions of a third order nonlinear difference equation with neutral delay." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4329--4354
Keywords
- Third order nonlinear difference equation with neutral delay
- uncountably many solutions
- Schauder fixed point theorem
- Krasnoselskii fixed point theorem.
MSC
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