Global asymptotic behavior for delay dynamic equations

We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.

Saved in:
Bibliographic Details
Published in:Nonlinear analysis 2007-04, Vol.66 (7), p.1633-1644
Main Authors: Anderson, Douglas R., Kenz, Zackary R.
Format: Article
Language:English
Subjects:
Asymptotic behavior
Delay
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematics
Nonlinear equation
Sciences and techniques of general use
Time scales
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643
cites cdi_FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643
container_end_page 1644
container_issue 7
container_start_page 1633
container_title Nonlinear analysis
container_volume 66
creator Anderson, Douglas R.
Kenz, Zackary R.
description We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.
doi_str_mv 10.1016/j.na.2006.02.014
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_29831385</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X06001003</els_id><sourcerecordid>29831385</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643</originalsourceid><addsrcrecordid>eNp1kM1LAzEQxYMoWKt3j3vR266TZJPNehPRKhS8KHgL2WSCKfvRJttC_3u3tODJwzCH-b03M4-QWwoFBSofVkVvCgYgC2AF0PKMzKiqeC4YFedkBlyyXJTy-5JcpbQCAFpxOSNy0Q6NaTOT9t16HMZgswZ_zC4MMfNTOWzNPnP73nTTCDdbM4ahT9fkwps24c2pz8nX68vn81u-_Fi8Pz8tc8uFGHNXWWZ9IwEtdaoxDDyvS6iplK5xllvhpou9Mr4CFCXKuqYKgSrPOKWy5HNyf_Rdx2GzxTTqLiSLbWt6HLZJs1pxypWYQDiCNg4pRfR6HUNn4l5T0IeA9Er3Rh8C0sD0FNAkuTt5m2RN66PpbUh_OiWqugI1cY9HDqdHdwGjTjZgb9GFiHbUbgj_L_kFWzd5qw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>29831385</pqid></control><display><type>article</type><title>Global asymptotic behavior for delay dynamic equations</title><source>Elsevier</source><source>Backfile Package - Mathematics (Legacy) [YMT]</source><creator>Anderson, Douglas R. ; Kenz, Zackary R.</creator><creatorcontrib>Anderson, Douglas R. ; Kenz, Zackary R.</creatorcontrib><description>We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2006.02.014</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Asymptotic behavior ; Delay ; Exact sciences and technology ; Global analysis, analysis on manifolds ; Mathematics ; Nonlinear equation ; Sciences and techniques of general use ; Time scales ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinear analysis, 2007-04, Vol.66 (7), p.1633-1644</ispartof><rights>2006 Elsevier Ltd</rights><rights>2007 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643</citedby><cites>FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X06001003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3564,27924,27925,46003</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=18579708$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Anderson, Douglas R.</creatorcontrib><creatorcontrib>Kenz, Zackary R.</creatorcontrib><title>Global asymptotic behavior for delay dynamic equations</title><title>Nonlinear analysis</title><description>We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.</description><subject>Asymptotic behavior</subject><subject>Delay</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Mathematics</subject><subject>Nonlinear equation</subject><subject>Sciences and techniques of general use</subject><subject>Time scales</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp1kM1LAzEQxYMoWKt3j3vR266TZJPNehPRKhS8KHgL2WSCKfvRJttC_3u3tODJwzCH-b03M4-QWwoFBSofVkVvCgYgC2AF0PKMzKiqeC4YFedkBlyyXJTy-5JcpbQCAFpxOSNy0Q6NaTOT9t16HMZgswZ_zC4MMfNTOWzNPnP73nTTCDdbM4ahT9fkwps24c2pz8nX68vn81u-_Fi8Pz8tc8uFGHNXWWZ9IwEtdaoxDDyvS6iplK5xllvhpou9Mr4CFCXKuqYKgSrPOKWy5HNyf_Rdx2GzxTTqLiSLbWt6HLZJs1pxypWYQDiCNg4pRfR6HUNn4l5T0IeA9Er3Rh8C0sD0FNAkuTt5m2RN66PpbUh_OiWqugI1cY9HDqdHdwGjTjZgb9GFiHbUbgj_L_kFWzd5qw</recordid><startdate>20070401</startdate><enddate>20070401</enddate><creator>Anderson, Douglas R.</creator><creator>Kenz, Zackary R.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20070401</creationdate><title>Global asymptotic behavior for delay dynamic equations</title><author>Anderson, Douglas R. ; Kenz, Zackary R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Asymptotic behavior</topic><topic>Delay</topic><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>Mathematics</topic><topic>Nonlinear equation</topic><topic>Sciences and techniques of general use</topic><topic>Time scales</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Anderson, Douglas R.</creatorcontrib><creatorcontrib>Kenz, Zackary R.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Anderson, Douglas R.</au><au>Kenz, Zackary R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global asymptotic behavior for delay dynamic equations</atitle><jtitle>Nonlinear analysis</jtitle><date>2007-04-01</date><risdate>2007</risdate><volume>66</volume><issue>7</issue><spage>1633</spage><epage>1644</epage><pages>1633-1644</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2006.02.014</doi><tpages>12</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0362-546X
ispartof Nonlinear analysis, 2007-04, Vol.66 (7), p.1633-1644
issn 0362-546X
1873-5215
language eng
recordid cdi_proquest_miscellaneous_29831385
source Elsevier; Backfile Package - Mathematics (Legacy) [YMT]
subjects Asymptotic behavior
Delay
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematics
Nonlinear equation
Sciences and techniques of general use
Time scales
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
title Global asymptotic behavior for delay dynamic equations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T19%3A31%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Global%20asymptotic%20behavior%20for%20delay%20dynamic%20equations&rft.jtitle=Nonlinear%20analysis&rft.au=Anderson,%20Douglas%20R.&rft.date=2007-04-01&rft.volume=66&rft.issue=7&rft.spage=1633&rft.epage=1644&rft.pages=1633-1644&rft.issn=0362-546X&rft.eissn=1873-5215&rft.coden=NOANDD&rft_id=info:doi/10.1016/j.na.2006.02.014&rft_dat=%3Cproquest_cross%3E29831385%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c355t-d7c2cfb60ec1d8ba20f39409166dbdc3c5d006f8af70e54e69918e018f2311643%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=29831385&rft_id=info:pmid/&rfr_iscdi=true