Title of article
A higher order nonlinear neutral differential equation
Author/Authors
Jiang ، Guojing - Vocational Technical College , Sun ، Wei Jiaokou No.1 Middle School , An ، Zhefu - Liaoning University , Zhao ، Liangshi - Liaoning Normal University
Pages
24
From page
675
To page
698
Abstract
This paper is concerned with the higher order nonlinear neutral differential equation\[[a(t)(x(t)+b(t)x(\tau(t))) ]^{(n1)}+f(t, x(g_1(t)),\ldots,x(g_k(t)))=c(t),\quad t\ge t_0.\] By dint of the LeraySchauder 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.
Keywords
Higher order nonlinear neutral differential equation , uncountably many bounded positive solutions , Leray , Schauder nonlinear alternative theorem , Rothe fixed point theorem
Journal title
Journal of Nonlinear Science and Applications
Serial Year
2019
Journal title
Journal of Nonlinear Science and Applications
Record number
2477106
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