# A higher order nonlinear neutral differential equation

Volume 12, Issue 10, pp 675--698
Publication Date: June 15, 2019 Submission Date: February 24, 2019 Revision Date: April 06, 2019 Accteptance Date: May 14, 2019
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### Authors

Guojing Jiang - Basic Teaching Department, Vocational Technical College, Dalian, Liaoning 116035, China. Wei Sun - Jiaokou No.1 Middle School, Lvliang, Shanxi 032400, China. Zhefu An - School of Mathematics, Liaoning University, Shenyang, Liaoning 110036, China. Liangshi Zhao - Center for Studies of Marine Economy and Sustainable Development, Liaoning Normal University, Dalian, Liaoning 116029, China.

### Abstract

This paper is concerned with the higher order nonlinear neutral differential equation $[a(t)(x(t)+b(t)x(\tau(t)))']^{(n-1)}+f(t, x(g_1(t)),\ldots, x(g_k(t)))=c(t),\quad t\ge t_0.$ By dint of the Leray-Schauder nonlinear alternative, Rothe fixed point theorem and some new techniques, we prove the existence of uncountably many bounded positive solutions for the equation. Several nontrivial examples are given to illustrate the applications and advantages of the results presented in this paper.

### Share and Cite

##### ISRP Style

Guojing Jiang, Wei Sun, Zhefu An, Liangshi Zhao, A higher order nonlinear neutral differential equation, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 10, 675--698

##### AMA Style

Jiang Guojing, Sun Wei, An Zhefu, Zhao Liangshi, A higher order nonlinear neutral differential equation. J. Nonlinear Sci. Appl. (2019); 12(10):675--698

##### Chicago/Turabian Style

Jiang, Guojing, Sun, Wei, An, Zhefu, Zhao, Liangshi. "A higher order nonlinear neutral differential equation." Journal of Nonlinear Sciences and Applications, 12, no. 10 (2019): 675--698

### Keywords

• Higher order nonlinear neutral differential equation
• uncountably many bounded positive solutions
• Leray-Schauder nonlinear alternative theorem
• Rothe fixed point theorem

•  34K40
•  35G20

### References

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