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Multiple positive solutions for nonlinear dynamical systems on a measure chain
In this paper, we consider the following dynamical system on a measure chain: u 1 ΔΔ(t)+f 1(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], u 2 ΔΔ(t)+f 2(t,u 1(σ(t)),u 2(σ(t)))=0, t∈[a,b], with the Sturm–Liouville boundary value conditions αu i(a)−βu i Δ(a)=0, γu i(σ(b))+δu i Δ(σ(b))=0 for i=1,2. Some results ar...
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| Published in: | Journal of computational and applied mathematics 2004-01, Vol.162 (2), p.421-430 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c399t-c2af70396c3f1db670cb4074ccbdc122da9c35af7ff7b510b7eb32a152212bb63 |
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| cites | cdi_FETCH-LOGICAL-c399t-c2af70396c3f1db670cb4074ccbdc122da9c35af7ff7b510b7eb32a152212bb63 |
| container_end_page | 430 |
| container_issue | 2 |
| container_start_page | 421 |
| container_title | Journal of computational and applied mathematics |
| container_volume | 162 |
| creator | Li, Wan-Tong Sun, Hong-Rui |
| description | In this paper, we consider the following dynamical system on a measure chain:
u
1
ΔΔ(t)+f
1(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
u
2
ΔΔ(t)+f
2(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
with the Sturm–Liouville boundary value conditions
αu
i(a)−βu
i
Δ(a)=0,
γu
i(σ(b))+δu
i
Δ(σ(b))=0
for
i=1,2.
Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem. |
| doi_str_mv | 10.1016/j.cam.2003.08.032 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_28228792</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377042703007568</els_id><sourcerecordid>28228792</sourcerecordid><originalsourceid>FETCH-LOGICAL-c399t-c2af70396c3f1db670cb4074ccbdc122da9c35af7ff7b510b7eb32a152212bb63</originalsourceid><addsrcrecordid>eNp9kEFv1DAQhS0EEkvLD-DmC9ySju1snKgnVBWoVOgFzpYzmQivEnvrSSrtv8fVVuqN01y-90bvE-KTglqBaq8ONfql1gCmhq4Go9-InepsXylru7diB8baChpt34sPzAcAaHvV7MSvn9u8huNM8pg4rOGJJKd5W0OKLKeUZUxxDpF8luMp-iWgnyWfeKWFZYrSy4U8b5kk_vUhXop3k5-ZPr7cC_Hn2-3vmx_V_cP3u5uv9xWavl8r1H6yYPoWzaTGobWAQwO2QRxGVFqPvkezL8w02WGvYLA0GO3VXmulh6E1F-LLufeY0-NGvLolMNI8-0hpY6c7rct6XUB1BjEn5kyTO-aw-HxyCtyzOXdwxZx7Nuegc8VcyXx-Kfdc5k7ZRwz8Gtw3re1aW7jrM0dl6VOg7BgDRaQxZMLVjSn858s_-EmEwQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>28228792</pqid></control><display><type>article</type><title>Multiple positive solutions for nonlinear dynamical systems on a measure chain</title><source>ScienceDirect Journals</source><creator>Li, Wan-Tong ; Sun, Hong-Rui</creator><creatorcontrib>Li, Wan-Tong ; Sun, Hong-Rui</creatorcontrib><description>In this paper, we consider the following dynamical system on a measure chain:
u
1
ΔΔ(t)+f
1(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
u
2
ΔΔ(t)+f
2(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
with the Sturm–Liouville boundary value conditions
αu
i(a)−βu
i
Δ(a)=0,
γu
i(σ(b))+δu
i
Δ(σ(b))=0
for
i=1,2.
Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2003.08.032</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Cone ; Exact sciences and technology ; Finite differences and functional equations ; Fixed point ; Mathematical analysis ; Mathematics ; Measure chain ; Ordinary differential equations ; Positive solution ; Sciences and techniques of general use</subject><ispartof>Journal of computational and applied mathematics, 2004-01, Vol.162 (2), p.421-430</ispartof><rights>2003 Elsevier B.V.</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c399t-c2af70396c3f1db670cb4074ccbdc122da9c35af7ff7b510b7eb32a152212bb63</citedby><cites>FETCH-LOGICAL-c399t-c2af70396c3f1db670cb4074ccbdc122da9c35af7ff7b510b7eb32a152212bb63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15467867$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Li, Wan-Tong</creatorcontrib><creatorcontrib>Sun, Hong-Rui</creatorcontrib><title>Multiple positive solutions for nonlinear dynamical systems on a measure chain</title><title>Journal of computational and applied mathematics</title><description>In this paper, we consider the following dynamical system on a measure chain:
u
1
ΔΔ(t)+f
1(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
u
2
ΔΔ(t)+f
2(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
with the Sturm–Liouville boundary value conditions
αu
i(a)−βu
i
Δ(a)=0,
γu
i(σ(b))+δu
i
Δ(σ(b))=0
for
i=1,2.
Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem.</description><subject>Cone</subject><subject>Exact sciences and technology</subject><subject>Finite differences and functional equations</subject><subject>Fixed point</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Measure chain</subject><subject>Ordinary differential equations</subject><subject>Positive solution</subject><subject>Sciences and techniques of general use</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNp9kEFv1DAQhS0EEkvLD-DmC9ySju1snKgnVBWoVOgFzpYzmQivEnvrSSrtv8fVVuqN01y-90bvE-KTglqBaq8ONfql1gCmhq4Go9-InepsXylru7diB8baChpt34sPzAcAaHvV7MSvn9u8huNM8pg4rOGJJKd5W0OKLKeUZUxxDpF8luMp-iWgnyWfeKWFZYrSy4U8b5kk_vUhXop3k5-ZPr7cC_Hn2-3vmx_V_cP3u5uv9xWavl8r1H6yYPoWzaTGobWAQwO2QRxGVFqPvkezL8w02WGvYLA0GO3VXmulh6E1F-LLufeY0-NGvLolMNI8-0hpY6c7rct6XUB1BjEn5kyTO-aw-HxyCtyzOXdwxZx7Nuegc8VcyXx-Kfdc5k7ZRwz8Gtw3re1aW7jrM0dl6VOg7BgDRaQxZMLVjSn858s_-EmEwQ</recordid><startdate>20040115</startdate><enddate>20040115</enddate><creator>Li, Wan-Tong</creator><creator>Sun, Hong-Rui</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20040115</creationdate><title>Multiple positive solutions for nonlinear dynamical systems on a measure chain</title><author>Li, Wan-Tong ; Sun, Hong-Rui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c399t-c2af70396c3f1db670cb4074ccbdc122da9c35af7ff7b510b7eb32a152212bb63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Cone</topic><topic>Exact sciences and technology</topic><topic>Finite differences and functional equations</topic><topic>Fixed point</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Measure chain</topic><topic>Ordinary differential equations</topic><topic>Positive solution</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Wan-Tong</creatorcontrib><creatorcontrib>Sun, Hong-Rui</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Wan-Tong</au><au>Sun, Hong-Rui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiple positive solutions for nonlinear dynamical systems on a measure chain</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2004-01-15</date><risdate>2004</risdate><volume>162</volume><issue>2</issue><spage>421</spage><epage>430</epage><pages>421-430</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>In this paper, we consider the following dynamical system on a measure chain:
u
1
ΔΔ(t)+f
1(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
u
2
ΔΔ(t)+f
2(t,u
1(σ(t)),u
2(σ(t)))=0,
t∈[a,b],
with the Sturm–Liouville boundary value conditions
αu
i(a)−βu
i
Δ(a)=0,
γu
i(σ(b))+δu
i
Δ(σ(b))=0
for
i=1,2.
Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2003.08.032</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 2004-01, Vol.162 (2), p.421-430 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_28228792 |
| source | ScienceDirect Journals |
| subjects | Cone Exact sciences and technology Finite differences and functional equations Fixed point Mathematical analysis Mathematics Measure chain Ordinary differential equations Positive solution Sciences and techniques of general use |
| title | Multiple positive solutions for nonlinear dynamical systems on a measure chain |
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