Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation

This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating thes...

Full description

Saved in:
Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.144-165
Main Authors: Kang, Shin Min, Ume, Jeong Sheok, Zhu, Jingjing, Liu, Zeqing
Format: Article
Language:English
Subjects:
Delay equations
Differential equations
Differential equations, Nonlinear
Fixed point theory
Iterative methods (Mathematics)
Mathematical research
Mathematics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-a545t-7c1fc516cc7ebcac1b0c7be949ad6e4d7b33f2c0b5168f842dca86367cc4cc673
container_end_page 165
container_issue 2014
container_start_page 144
container_title Abstract and Applied Analysis
container_volume 2014
creator Kang, Shin Min
Ume, Jeong Sheok
Zhu, Jingjing
Liu, Zeqing
description This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.
doi_str_mv 10.1155/2014/105719
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_2291296879fc4c33876c03b4d22b4cd2</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A426542731</galeid><airiti_id>P20160825001_201412_201609080014_201609080014_144_165</airiti_id><doaj_id>oai_doaj_org_article_2291296879fc4c33876c03b4d22b4cd2</doaj_id><sourcerecordid>A426542731</sourcerecordid><originalsourceid>FETCH-LOGICAL-a545t-7c1fc516cc7ebcac1b0c7be949ad6e4d7b33f2c0b5168f842dca86367cc4cc673</originalsourceid><addsrcrecordid>eNqFkk1v1DAQhiMEEqVw4o4icaPa1t9OblTbFlZaaCXo2Zr4o_UqtVsnAfXfM7tZFXrCkuXxq2dej0dTVe8pOaZUyhNGqDihRGravqgOqGr0ggjSvsSYNHLBuZavqzfDsCGEcC3EQRWu8hDH-MvXP3I_jTGnoYbk6m-QUr0afYFZy6GG-iJPZbytL4vzpf6eUx-TB4z8NBbo6zPfw2N9FkPwxacxonT-MO0M3lavAvSDf7c_D6vri_Ofy6-L9eWX1fJ0vQAp5LjQlgYrqbJW-86CpR2xuvOtaMEpL5zuOA_Mkg6ZJjSCOQuN4kpbK6xVmh9Wq9nXZdiY-xLvoDyaDNHshFxuDJQx2t4bxlrKWmxRGzCZ80YrS3gnHGOdsI6h1-fZ677kjbejn2wf3TPT5fV6r-4PADBUUMa0Jkyhxccni4fJD6PZYAsTdsBQKTQuyVqkjmfqBrCumELGduLvwfm7aHPyIaJ-KpiSgmlOMeFoTrAlD0Px4akoSsx2EMx2EMw8CEh_munbmBz8jv-BP8ywR8QH-AfmfC52PQMQCw7O3w9doY0iDZOE0J0lZWYntaQh2xeeXajArST_Ax1U0IM</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1547777529</pqid></control><display><type>article</type><title>Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation</title><source>Wiley Online Library</source><source>Publicly Available Content Database</source><creator>Kang, Shin Min ; Ume, Jeong Sheok ; Zhu, Jingjing ; Liu, Zeqing</creator><contributor>Peterson, Allan</contributor><creatorcontrib>Kang, Shin Min ; Ume, Jeong Sheok ; Zhu, Jingjing ; Liu, Zeqing ; Peterson, Allan</creatorcontrib><description>This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.</description><identifier>ISSN: 1085-3375</identifier><identifier>EISSN: 1687-0409</identifier><identifier>DOI: 10.1155/2014/105719</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Limiteds</publisher><subject>Delay equations ; Differential equations ; Differential equations, Nonlinear ; Fixed point theory ; Iterative methods (Mathematics) ; Mathematical research ; Mathematics</subject><ispartof>Abstract and Applied Analysis, 2014-01, Vol.2014 (2014), p.144-165</ispartof><rights>Copyright © 2014 Zeqing Liu et al.</rights><rights>COPYRIGHT 2014 John Wiley &amp; Sons, Inc.</rights><rights>Copyright © 2014 Zeqing Liu et al. Zeqing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><rights>Copyright 2014 Hindawi Publishing Corporation</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-a545t-7c1fc516cc7ebcac1b0c7be949ad6e4d7b33f2c0b5168f842dca86367cc4cc673</cites><orcidid>0000-0001-5919-8822 ; 0000-0002-5294-4447</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1547777529/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1547777529?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,881,25731,27901,27902,36989,44566,74869</link.rule.ids></links><search><contributor>Peterson, Allan</contributor><creatorcontrib>Kang, Shin Min</creatorcontrib><creatorcontrib>Ume, Jeong Sheok</creatorcontrib><creatorcontrib>Zhu, Jingjing</creatorcontrib><creatorcontrib>Liu, Zeqing</creatorcontrib><title>Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation</title><title>Abstract and Applied Analysis</title><description>This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.</description><subject>Delay equations</subject><subject>Differential equations</subject><subject>Differential equations, Nonlinear</subject><subject>Fixed point theory</subject><subject>Iterative methods (Mathematics)</subject><subject>Mathematical research</subject><subject>Mathematics</subject><issn>1085-3375</issn><issn>1687-0409</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNqFkk1v1DAQhiMEEqVw4o4icaPa1t9OblTbFlZaaCXo2Zr4o_UqtVsnAfXfM7tZFXrCkuXxq2dej0dTVe8pOaZUyhNGqDihRGravqgOqGr0ggjSvsSYNHLBuZavqzfDsCGEcC3EQRWu8hDH-MvXP3I_jTGnoYbk6m-QUr0afYFZy6GG-iJPZbytL4vzpf6eUx-TB4z8NBbo6zPfw2N9FkPwxacxonT-MO0M3lavAvSDf7c_D6vri_Ofy6-L9eWX1fJ0vQAp5LjQlgYrqbJW-86CpR2xuvOtaMEpL5zuOA_Mkg6ZJjSCOQuN4kpbK6xVmh9Wq9nXZdiY-xLvoDyaDNHshFxuDJQx2t4bxlrKWmxRGzCZ80YrS3gnHGOdsI6h1-fZ677kjbejn2wf3TPT5fV6r-4PADBUUMa0Jkyhxccni4fJD6PZYAsTdsBQKTQuyVqkjmfqBrCumELGduLvwfm7aHPyIaJ-KpiSgmlOMeFoTrAlD0Px4akoSsx2EMx2EMw8CEh_munbmBz8jv-BP8ywR8QH-AfmfC52PQMQCw7O3w9doY0iDZOE0J0lZWYntaQh2xeeXajArST_Ax1U0IM</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Kang, Shin Min</creator><creator>Ume, Jeong Sheok</creator><creator>Zhu, Jingjing</creator><creator>Liu, Zeqing</creator><general>Hindawi Limiteds</general><general>Hindawi Publishing Corporation</general><general>John Wiley &amp; Sons, Inc</general><general>Hindawi Limited</general><scope>188</scope><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0001-5919-8822</orcidid><orcidid>https://orcid.org/0000-0002-5294-4447</orcidid></search><sort><creationdate>20140101</creationdate><title>Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation</title><author>Kang, Shin Min ; Ume, Jeong Sheok ; Zhu, Jingjing ; Liu, Zeqing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a545t-7c1fc516cc7ebcac1b0c7be949ad6e4d7b33f2c0b5168f842dca86367cc4cc673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Delay equations</topic><topic>Differential equations</topic><topic>Differential equations, Nonlinear</topic><topic>Fixed point theory</topic><topic>Iterative methods (Mathematics)</topic><topic>Mathematical research</topic><topic>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kang, Shin Min</creatorcontrib><creatorcontrib>Ume, Jeong Sheok</creatorcontrib><creatorcontrib>Zhu, Jingjing</creatorcontrib><creatorcontrib>Liu, Zeqing</creatorcontrib><collection>Airiti Library</collection><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East &amp; Africa Database</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Abstract and Applied Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kang, Shin Min</au><au>Ume, Jeong Sheok</au><au>Zhu, Jingjing</au><au>Liu, Zeqing</au><au>Peterson, Allan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation</atitle><jtitle>Abstract and Applied Analysis</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>2014</volume><issue>2014</issue><spage>144</spage><epage>165</epage><pages>144-165</pages><issn>1085-3375</issn><eissn>1687-0409</eissn><abstract>This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Limiteds</pub><doi>10.1155/2014/105719</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0001-5919-8822</orcidid><orcidid>https://orcid.org/0000-0002-5294-4447</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1085-3375
ispartof Abstract and Applied Analysis, 2014-01, Vol.2014 (2014), p.144-165
issn 1085-3375
1687-0409
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_2291296879fc4c33876c03b4d22b4cd2
source Wiley Online Library; Publicly Available Content Database
subjects Delay equations
Differential equations
Differential equations, Nonlinear
Fixed point theory
Iterative methods (Mathematics)
Mathematical research
Mathematics
title Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T22%3A08%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Positive%20Solutions%20and%20Mann%20Iterations%20of%20a%20Fourth%20Order%20Nonlinear%20Neutral%20Delay%20Differential%20Equation&rft.jtitle=Abstract%20and%20Applied%20Analysis&rft.au=Kang,%20Shin%20Min&rft.date=2014-01-01&rft.volume=2014&rft.issue=2014&rft.spage=144&rft.epage=165&rft.pages=144-165&rft.issn=1085-3375&rft.eissn=1687-0409&rft_id=info:doi/10.1155/2014/105719&rft_dat=%3Cgale_doaj_%3EA426542731%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a545t-7c1fc516cc7ebcac1b0c7be949ad6e4d7b33f2c0b5168f842dca86367cc4cc673%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1547777529&rft_id=info:pmid/&rft_galeid=A426542731&rft_airiti_id=P20160825001_201412_201609080014_201609080014_144_165&rfr_iscdi=true