Geodesic
A higher order nonlinear neutral differential equation
Jiang, Guojing 1 ; Sun, Wei 2 ; An, Zhefu 3 ; Zhao, Liangshi 4
1 Basic Teaching Department, Vocational Technical College, Dalian, Liaoning 116035, China
2 Jiaokou No.1 Middle School, Lvliang, Shanxi 032400, China
3 School of Mathematics, Liaoning University, Shenyang, Liaoning 110036, China
4 Center for Studies of Marine Economy and Sustainable Development, Liaoning Normal University, Dalian, Liaoning 116029, China
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 10, p. 675-698.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.012.10.06
Classification : 34K40, 35G20
Keywords: Higher order nonlinear neutral differential equation, uncountably many bounded positive solutions, Leray-Schauder nonlinear alternative theorem, Rothe fixed point theorem

Jiang, Guojing  1 ; Sun, Wei  2 ; An, Zhefu  3 ; Zhao, Liangshi  4

1 Basic Teaching Department, Vocational Technical College, Dalian, Liaoning 116035, China
2 Jiaokou No.1 Middle School, Lvliang, Shanxi 032400, China
3 School of Mathematics, Liaoning University, Shenyang, Liaoning 110036, China
4 Center for Studies of Marine Economy and Sustainable Development, Liaoning Normal University, Dalian, Liaoning 116029, China 
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Jiang, Guojing ; Sun, Wei ; An, Zhefu ; Zhao, Liangshi . A higher order nonlinear neutral differential equation. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 10, p. 675-698. doi : 10.22436/jnsa.012.10.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.10.06/

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