New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.

Saved in:
Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.140-144-713
Main Authors: Liu, Shouhua, Zhang, Quanxin
Format: Article
Language:English
Subjects:
Continuity
Damping
Differential equations, Nonlinear
Mathematical functions
Mathematical research
Theorems
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-a549t-1f82f92466a988d5eb3324a37d706603451745db95b666e8357fc04102e79a13
container_end_page 144-713
container_issue 2014
container_start_page 140
container_title Abstract and Applied Analysis
container_volume 2014
creator Liu, Shouhua
Zhang, Quanxin
description We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.
doi_str_mv 10.1155/2014/475428
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_ae16da7f1c944a2f8a763357dc5150a7</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A426543401</galeid><airiti_id>P20160825001_201412_201609080014_201609080014_140_144_713</airiti_id><doaj_id>oai_doaj_org_article_ae16da7f1c944a2f8a763357dc5150a7</doaj_id><sourcerecordid>A426543401</sourcerecordid><originalsourceid>FETCH-LOGICAL-a549t-1f82f92466a988d5eb3324a37d706603451745db95b666e8357fc04102e79a13</originalsourceid><addsrcrecordid>eNqFks1v0zAUwCMEEmNw4o4scQNl87eTG6MbMKlaJ62czas_Wldp3DkpVf97nKYa7ISiyM7Tz7_n9_KK4j3BF4QIcUkx4ZdcCU6rF8UZkZUqMcf1y7zHlSgZU-J18abr1hhjpjg_K37duT2adSY0DfQxHdBXt4LfISYUPXpwJra2nCXrErqLbRNaBwldH1rYBINuHnfQh9h2aB_6FbqGzTa0SxRbNA8bhx4MNK57W7zy0HTu3Wk9L-bfbuaTH-V09v12cjUtQfC6L4mvqK8plxLqqrLCLRijHJiyCkuJGRdEcWEXtVhIKV3FhPIGc4KpUzUQdl7cjlobYa23KWwgHXSEoI-BmJYaUh9M4zQ4Ii0oT0zNOVBfgZIs-6wRRGBQ2fVldG1TXDvTu51pgn0mnfycnqKnBQA04VRgXuOqyoqPT4rHnet6vY671OYG6PyfhjKFwpm6GKll7pQOrY99ApMf63J_Y-t8yPErTqXgjOOhys_jAZNi1yXnny5FsB4mQA8ToMcJyPSnkV6F1sI-_Af-MMIuI87DPzDhmA6570cAQgp9-FvQfdZIXOXaMTkqCdXHUO4EHjI8-8iy_HKtCGN_ADUezJ4</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1552466570</pqid></control><display><type>article</type><title>New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales</title><source>Open Access: Wiley-Blackwell Open Access Journals</source><source>Publicly Available Content (ProQuest)</source><creator>Liu, Shouhua ; Zhang, Quanxin</creator><contributor>Li, Tongxing</contributor><creatorcontrib>Liu, Shouhua ; Zhang, Quanxin ; Li, Tongxing</creatorcontrib><description>We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.</description><identifier>ISSN: 1085-3375</identifier><identifier>EISSN: 1687-0409</identifier><identifier>DOI: 10.1155/2014/475428</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Limiteds</publisher><subject>Continuity ; Damping ; Differential equations, Nonlinear ; Mathematical functions ; Mathematical research ; Theorems</subject><ispartof>Abstract and Applied Analysis, 2014-01, Vol.2014 (2014), p.140-144-713</ispartof><rights>Copyright © 2014 Shouhua Liu and Quanxin Zhang.</rights><rights>COPYRIGHT 2014 John Wiley &amp; Sons, Inc.</rights><rights>Copyright © 2014 Shouhua Liu and Quanxin Zhang. Shouhua 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 2013 Hindawi Publishing Corporation</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-a549t-1f82f92466a988d5eb3324a37d706603451745db95b666e8357fc04102e79a13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1552466570/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1552466570?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>230,314,780,784,885,25753,27924,27925,37012,44590,75126</link.rule.ids></links><search><contributor>Li, Tongxing</contributor><creatorcontrib>Liu, Shouhua</creatorcontrib><creatorcontrib>Zhang, Quanxin</creatorcontrib><title>New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales</title><title>Abstract and Applied Analysis</title><description>We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.</description><subject>Continuity</subject><subject>Damping</subject><subject>Differential equations, Nonlinear</subject><subject>Mathematical functions</subject><subject>Mathematical research</subject><subject>Theorems</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>eNqFks1v0zAUwCMEEmNw4o4scQNl87eTG6MbMKlaJ62czas_Wldp3DkpVf97nKYa7ISiyM7Tz7_n9_KK4j3BF4QIcUkx4ZdcCU6rF8UZkZUqMcf1y7zHlSgZU-J18abr1hhjpjg_K37duT2adSY0DfQxHdBXt4LfISYUPXpwJra2nCXrErqLbRNaBwldH1rYBINuHnfQh9h2aB_6FbqGzTa0SxRbNA8bhx4MNK57W7zy0HTu3Wk9L-bfbuaTH-V09v12cjUtQfC6L4mvqK8plxLqqrLCLRijHJiyCkuJGRdEcWEXtVhIKV3FhPIGc4KpUzUQdl7cjlobYa23KWwgHXSEoI-BmJYaUh9M4zQ4Ii0oT0zNOVBfgZIs-6wRRGBQ2fVldG1TXDvTu51pgn0mnfycnqKnBQA04VRgXuOqyoqPT4rHnet6vY671OYG6PyfhjKFwpm6GKll7pQOrY99ApMf63J_Y-t8yPErTqXgjOOhys_jAZNi1yXnny5FsB4mQA8ToMcJyPSnkV6F1sI-_Af-MMIuI87DPzDhmA6570cAQgp9-FvQfdZIXOXaMTkqCdXHUO4EHjI8-8iy_HKtCGN_ADUezJ4</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Liu, Shouhua</creator><creator>Zhang, Quanxin</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></search><sort><creationdate>20140101</creationdate><title>New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales</title><author>Liu, Shouhua ; Zhang, Quanxin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a549t-1f82f92466a988d5eb3324a37d706603451745db95b666e8357fc04102e79a13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Continuity</topic><topic>Damping</topic><topic>Differential equations, Nonlinear</topic><topic>Mathematical functions</topic><topic>Mathematical research</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Shouhua</creatorcontrib><creatorcontrib>Zhang, Quanxin</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</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 Korea</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 (ProQuest)</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>Liu, Shouhua</au><au>Zhang, Quanxin</au><au>Li, Tongxing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales</atitle><jtitle>Abstract and Applied Analysis</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>2014</volume><issue>2014</issue><spage>140</spage><epage>144-713</epage><pages>140-144-713</pages><issn>1085-3375</issn><eissn>1687-0409</eissn><abstract>We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Limiteds</pub><doi>10.1155/2014/475428</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1085-3375
ispartof Abstract and Applied Analysis, 2014-01, Vol.2014 (2014), p.140-144-713
issn 1085-3375
1687-0409
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_ae16da7f1c944a2f8a763357dc5150a7
source Open Access: Wiley-Blackwell Open Access Journals; Publicly Available Content (ProQuest)
subjects Continuity
Damping
Differential equations, Nonlinear
Mathematical functions
Mathematical research
Theorems
title New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T19%3A31%3A03IST&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=New%20Oscillatory%20Behavior%20of%20Second-Order%20Nonlinear%20Dynamic%20Equations%20with%20Damping%20on%20Time%20Scales&rft.jtitle=Abstract%20and%20Applied%20Analysis&rft.au=Liu,%20Shouhua&rft.date=2014-01-01&rft.volume=2014&rft.issue=2014&rft.spage=140&rft.epage=144-713&rft.pages=140-144-713&rft.issn=1085-3375&rft.eissn=1687-0409&rft_id=info:doi/10.1155/2014/475428&rft_dat=%3Cgale_doaj_%3EA426543401%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a549t-1f82f92466a988d5eb3324a37d706603451745db95b666e8357fc04102e79a13%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1552466570&rft_id=info:pmid/&rft_galeid=A426543401&rft_airiti_id=P20160825001_201412_201609080014_201609080014_140_144_713&rfr_iscdi=true