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Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable
This article deals with integral boundary value problems of the second-order differential equations { u ″ ( t ) + a ( t ) u ′ ( t ) + b ( t ) u ( t ) + f ( t , u ( t ) ) = 0 , t ∈ J + , u ( 0 ) = ∫ 0 1 g ( s ) u ( s ) d s , u ( 1 ) = ∫ 0 1 h ( s ) u ( s ) d s , where a ∈ C ( J ) , b ∈ C ( J , R − )...
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| Published in: | Boundary value problems 2017-06, Vol.2017 (1), p.1-10, Article 90 |
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| Main Authors: | , |
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| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c425t-61ca8389d62d14ac6e371abe8a8988a87d25266dc3faa4d981019f128c3071123 |
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| cites | cdi_FETCH-LOGICAL-c425t-61ca8389d62d14ac6e371abe8a8988a87d25266dc3faa4d981019f128c3071123 |
| container_end_page | 10 |
| container_issue | 1 |
| container_start_page | 1 |
| container_title | Boundary value problems |
| container_volume | 2017 |
| creator | Zhong, Qiuyan Zhang, Xingqiu |
| description | This article deals with integral boundary value problems of the second-order differential equations
{
u
″
(
t
)
+
a
(
t
)
u
′
(
t
)
+
b
(
t
)
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
t
∈
J
+
,
u
(
0
)
=
∫
0
1
g
(
s
)
u
(
s
)
d
s
,
u
(
1
)
=
∫
0
1
h
(
s
)
u
(
s
)
d
s
,
where
a
∈
C
(
J
)
,
b
∈
C
(
J
,
R
−
)
,
f
∈
C
(
J
+
×
R
+
,
R
+
)
and
g
,
h
∈
L
1
(
J
)
are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity
f
permits the singularity on the space variable. |
| doi_str_mv | 10.1186/s13661-017-0822-9 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_73e9e567c56b49929bacc30a1bf86160</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_73e9e567c56b49929bacc30a1bf86160</doaj_id><sourcerecordid>1910573758</sourcerecordid><originalsourceid>FETCH-LOGICAL-c425t-61ca8389d62d14ac6e371abe8a8988a87d25266dc3faa4d981019f128c3071123</originalsourceid><addsrcrecordid>eNp1kc1u3SAQha2qlZqmfYDukLJ2y4DNz7KKkiZSomzSNRoDvuWKa24Bp8rbh8RVlU02DIzO-ZjR6bqvQL8BKPG9ABcCegqyp4qxXr_rTkAo2TMp6ftX94_dp1L2lHLNB3bS1ds11nCMnhxTCTU8eFJSXGtISyE1tcehdbxNi-tTdj6TsFS_yxjJlNbFYX4kDxjX5s9piv5QyN9Qf5MSlt0aMYf6SNJCyhGtb8IcsIk-dx9mjMV_-VdPu1-XF_fnV_3N3c_r8x83vR3YWHsBFhVX2gnmYEArPJeAk1eotGqHdGxkQjjLZ8TBaQUU9AxMWU4lAOOn3fXGdQn35pjDoY1rEgbz0kh5ZzDXYKM3knvtRyHtKKZBa6YntA2DMM1KgKCNdbax2p5_Vl-q2ac1L218AxroKLkcVVPBprI5lZL9_P9XoOY5KLMFZVpQ5jkoo5uHbZ7StMvO51fkN01P5xKXZA</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1910573758</pqid></control><display><type>article</type><title>Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable</title><source>Publicly Available Content Database</source><source>Springer Nature - SpringerLink Journals - Fully Open Access </source><creator>Zhong, Qiuyan ; Zhang, Xingqiu</creator><creatorcontrib>Zhong, Qiuyan ; Zhang, Xingqiu</creatorcontrib><description>This article deals with integral boundary value problems of the second-order differential equations
{
u
″
(
t
)
+
a
(
t
)
u
′
(
t
)
+
b
(
t
)
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
t
∈
J
+
,
u
(
0
)
=
∫
0
1
g
(
s
)
u
(
s
)
d
s
,
u
(
1
)
=
∫
0
1
h
(
s
)
u
(
s
)
d
s
,
where
a
∈
C
(
J
)
,
b
∈
C
(
J
,
R
−
)
,
f
∈
C
(
J
+
×
R
+
,
R
+
)
and
g
,
h
∈
L
1
(
J
)
are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity
f
permits the singularity on the space variable.</description><identifier>ISSN: 1687-2770</identifier><identifier>ISSN: 1687-2762</identifier><identifier>EISSN: 1687-2770</identifier><identifier>DOI: 10.1186/s13661-017-0822-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Approximations and Expansions ; Boundary value problems ; cone ; Cones ; Difference and Functional Equations ; Differential equations ; integral boundary value ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Ordinary Differential Equations ; Partial Differential Equations ; singularity ; two positive solutions</subject><ispartof>Boundary value problems, 2017-06, Vol.2017 (1), p.1-10, Article 90</ispartof><rights>The Author(s) 2017</rights><rights>Boundary Value Problems is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c425t-61ca8389d62d14ac6e371abe8a8988a87d25266dc3faa4d981019f128c3071123</citedby><cites>FETCH-LOGICAL-c425t-61ca8389d62d14ac6e371abe8a8988a87d25266dc3faa4d981019f128c3071123</cites><orcidid>0000-0002-5832-2892</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1910573758/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1910573758?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,25731,27901,27902,36989,44566,74869</link.rule.ids></links><search><creatorcontrib>Zhong, Qiuyan</creatorcontrib><creatorcontrib>Zhang, Xingqiu</creatorcontrib><title>Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable</title><title>Boundary value problems</title><addtitle>Bound Value Probl</addtitle><description>This article deals with integral boundary value problems of the second-order differential equations
{
u
″
(
t
)
+
a
(
t
)
u
′
(
t
)
+
b
(
t
)
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
t
∈
J
+
,
u
(
0
)
=
∫
0
1
g
(
s
)
u
(
s
)
d
s
,
u
(
1
)
=
∫
0
1
h
(
s
)
u
(
s
)
d
s
,
where
a
∈
C
(
J
)
,
b
∈
C
(
J
,
R
−
)
,
f
∈
C
(
J
+
×
R
+
,
R
+
)
and
g
,
h
∈
L
1
(
J
)
are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity
f
permits the singularity on the space variable.</description><subject>Analysis</subject><subject>Approximations and Expansions</subject><subject>Boundary value problems</subject><subject>cone</subject><subject>Cones</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>integral boundary value</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>singularity</subject><subject>two positive solutions</subject><issn>1687-2770</issn><issn>1687-2762</issn><issn>1687-2770</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp1kc1u3SAQha2qlZqmfYDukLJ2y4DNz7KKkiZSomzSNRoDvuWKa24Bp8rbh8RVlU02DIzO-ZjR6bqvQL8BKPG9ABcCegqyp4qxXr_rTkAo2TMp6ftX94_dp1L2lHLNB3bS1ds11nCMnhxTCTU8eFJSXGtISyE1tcehdbxNi-tTdj6TsFS_yxjJlNbFYX4kDxjX5s9piv5QyN9Qf5MSlt0aMYf6SNJCyhGtb8IcsIk-dx9mjMV_-VdPu1-XF_fnV_3N3c_r8x83vR3YWHsBFhVX2gnmYEArPJeAk1eotGqHdGxkQjjLZ8TBaQUU9AxMWU4lAOOn3fXGdQn35pjDoY1rEgbz0kh5ZzDXYKM3knvtRyHtKKZBa6YntA2DMM1KgKCNdbax2p5_Vl-q2ac1L218AxroKLkcVVPBprI5lZL9_P9XoOY5KLMFZVpQ5jkoo5uHbZ7StMvO51fkN01P5xKXZA</recordid><startdate>20170617</startdate><enddate>20170617</enddate><creator>Zhong, Qiuyan</creator><creator>Zhang, Xingqiu</creator><general>Springer International Publishing</general><general>Hindawi Limited</general><general>SpringerOpen</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</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>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</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>Q9U</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0002-5832-2892</orcidid></search><sort><creationdate>20170617</creationdate><title>Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable</title><author>Zhong, Qiuyan ; Zhang, Xingqiu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c425t-61ca8389d62d14ac6e371abe8a8988a87d25266dc3faa4d981019f128c3071123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Approximations and Expansions</topic><topic>Boundary value problems</topic><topic>cone</topic><topic>Cones</topic><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>integral boundary value</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>singularity</topic><topic>two positive solutions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhong, Qiuyan</creatorcontrib><creatorcontrib>Zhang, Xingqiu</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Database (Proquest)</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</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>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>ProQuest Engineering Database</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & 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>ProQuest Central Basic</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Boundary value problems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhong, Qiuyan</au><au>Zhang, Xingqiu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable</atitle><jtitle>Boundary value problems</jtitle><stitle>Bound Value Probl</stitle><date>2017-06-17</date><risdate>2017</risdate><volume>2017</volume><issue>1</issue><spage>1</spage><epage>10</epage><pages>1-10</pages><artnum>90</artnum><issn>1687-2770</issn><issn>1687-2762</issn><eissn>1687-2770</eissn><abstract>This article deals with integral boundary value problems of the second-order differential equations
{
u
″
(
t
)
+
a
(
t
)
u
′
(
t
)
+
b
(
t
)
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
t
∈
J
+
,
u
(
0
)
=
∫
0
1
g
(
s
)
u
(
s
)
d
s
,
u
(
1
)
=
∫
0
1
h
(
s
)
u
(
s
)
d
s
,
where
a
∈
C
(
J
)
,
b
∈
C
(
J
,
R
−
)
,
f
∈
C
(
J
+
×
R
+
,
R
+
)
and
g
,
h
∈
L
1
(
J
)
are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity
f
permits the singularity on the space variable.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13661-017-0822-9</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-5832-2892</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1687-2770 |
| ispartof | Boundary value problems, 2017-06, Vol.2017 (1), p.1-10, Article 90 |
| issn | 1687-2770 1687-2762 1687-2770 |
| language | eng |
| recordid | cdi_doaj_primary_oai_doaj_org_article_73e9e567c56b49929bacc30a1bf86160 |
| source | Publicly Available Content Database; Springer Nature - SpringerLink Journals - Fully Open Access |
| subjects | Analysis Approximations and Expansions Boundary value problems cone Cones Difference and Functional Equations Differential equations integral boundary value Mathematical analysis Mathematics Mathematics and Statistics Nonlinearity Ordinary Differential Equations Partial Differential Equations singularity two positive solutions |
| title | Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable |
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