{"title":"A higher order nonlinear neutral differential equation","authors":"G. Jiang, Weiling Sun, Z. An, Liangshi Zhao","doi":"10.22436/JNSA.012.10.06","DOIUrl":null,"url":null,"abstract":"This paper is concerned with the higher order nonlinear neutral differential equation [a(t)(x(t) + b(t)x(τ(t))) ′](n−1) + f(t, x(g1(t)), . . . , x(gk(t))) = c(t), t > t0. 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.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.012.10.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with the higher order nonlinear neutral differential equation [a(t)(x(t) + b(t)x(τ(t))) ′](n−1) + f(t, x(g1(t)), . . . , x(gk(t))) = c(t), t > t0. 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.
期刊介绍：
The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.
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