Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations
In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations x ′ ′ + α x ′ + a ( t ) x n - b ( t ) x n + 1 + c ( t ) x n + 2 = 0 , where α ∈ R is a constant, n is a finite positive integer, and a ( t ), b ( t ), c (...
Gespeichert in:
| Veröffentlicht in: | Monatshefte für Mathematik 2020-12, Vol.193 (4), p.829-843 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 843 |
|---|---|
| container_issue | 4 |
| container_start_page | 829 |
| container_title | Monatshefte für Mathematik |
| container_volume | 193 |
| creator | Han, Xiaoling Yang, Hujun |
| description | In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations
x
′
′
+
α
x
′
+
a
(
t
)
x
n
-
b
(
t
)
x
n
+
1
+
c
(
t
)
x
n
+
2
=
0
,
where
α
∈
R
is a constant,
n
is a finite positive integer, and
a
(
t
),
b
(
t
),
c
(
t
) are continuous periodic functions. By using Mawhin’s continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations. |
| doi_str_mv | 10.1007/s00605-020-01465-w |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2450417232</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2450417232</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-9604df2985dfeae3ab3bd0248e8d426b50d82f24730c46a464ff52ba25a04e623</originalsourceid><addsrcrecordid>eNp9kMtKAzEUhoMoWKsv4CrgOnpy7cxSSr2A4EbXIZOLpEwnbTJD7ds77Qju3Jyz-b7_HH6EbincU4DFQwFQIAkwIECFkmR_hmZUcEUkVPQczQCYIjWT8hJdlbIGAMpVPUPt6juW3nfWY9M5vBnaPm7baGN_wCngrc8xuWhxSe3Qx9QVHFLGBtvWlHIkirepcyRl5zMeZ-xMPmAXQ_DZd300Lfa7wZzca3QRTFv8ze-eo8-n1cfyhby9P78uH9-I5bTuSa1AuMDqSrrgjeem4Y0DJipfOcFUI8FVLDCx4GCFMkKJECRrDJMGhFeMz9HdlLvNaTf40ut1GnI3ntRMSBB0wfiRYhNlcyol-6C3OW7G7zUFfWxVT63qsVV9alXvR4lPUhnh7svnv-h_rB_SCHzR</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2450417232</pqid></control><display><type>article</type><title>Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations</title><source>SpringerLink Journals - AutoHoldings</source><creator>Han, Xiaoling ; Yang, Hujun</creator><creatorcontrib>Han, Xiaoling ; Yang, Hujun</creatorcontrib><description>In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations
x
′
′
+
α
x
′
+
a
(
t
)
x
n
-
b
(
t
)
x
n
+
1
+
c
(
t
)
x
n
+
2
=
0
,
where
α
∈
R
is a constant,
n
is a finite positive integer, and
a
(
t
),
b
(
t
),
c
(
t
) are continuous periodic functions. By using Mawhin’s continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations.</description><identifier>ISSN: 0026-9255</identifier><identifier>EISSN: 1436-5081</identifier><identifier>DOI: 10.1007/s00605-020-01465-w</identifier><language>eng</language><publisher>Vienna: Springer Vienna</publisher><subject>Continuity (mathematics) ; Differential equations ; Existence theorems ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Ordinary differential equations ; Periodic functions</subject><ispartof>Monatshefte für Mathematik, 2020-12, Vol.193 (4), p.829-843</ispartof><rights>Springer-Verlag GmbH Austria, part of Springer Nature 2020</rights><rights>Springer-Verlag GmbH Austria, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-9604df2985dfeae3ab3bd0248e8d426b50d82f24730c46a464ff52ba25a04e623</citedby><cites>FETCH-LOGICAL-c319t-9604df2985dfeae3ab3bd0248e8d426b50d82f24730c46a464ff52ba25a04e623</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00605-020-01465-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00605-020-01465-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Han, Xiaoling</creatorcontrib><creatorcontrib>Yang, Hujun</creatorcontrib><title>Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations</title><title>Monatshefte für Mathematik</title><addtitle>Monatsh Math</addtitle><description>In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations
x
′
′
+
α
x
′
+
a
(
t
)
x
n
-
b
(
t
)
x
n
+
1
+
c
(
t
)
x
n
+
2
=
0
,
where
α
∈
R
is a constant,
n
is a finite positive integer, and
a
(
t
),
b
(
t
),
c
(
t
) are continuous periodic functions. By using Mawhin’s continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations.</description><subject>Continuity (mathematics)</subject><subject>Differential equations</subject><subject>Existence theorems</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary differential equations</subject><subject>Periodic functions</subject><issn>0026-9255</issn><issn>1436-5081</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsv4CrgOnpy7cxSSr2A4EbXIZOLpEwnbTJD7ds77Qju3Jyz-b7_HH6EbincU4DFQwFQIAkwIECFkmR_hmZUcEUkVPQczQCYIjWT8hJdlbIGAMpVPUPt6juW3nfWY9M5vBnaPm7baGN_wCngrc8xuWhxSe3Qx9QVHFLGBtvWlHIkirepcyRl5zMeZ-xMPmAXQ_DZd300Lfa7wZzca3QRTFv8ze-eo8-n1cfyhby9P78uH9-I5bTuSa1AuMDqSrrgjeem4Y0DJipfOcFUI8FVLDCx4GCFMkKJECRrDJMGhFeMz9HdlLvNaTf40ut1GnI3ntRMSBB0wfiRYhNlcyol-6C3OW7G7zUFfWxVT63qsVV9alXvR4lPUhnh7svnv-h_rB_SCHzR</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Han, Xiaoling</creator><creator>Yang, Hujun</creator><general>Springer Vienna</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201201</creationdate><title>Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations</title><author>Han, Xiaoling ; Yang, Hujun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-9604df2985dfeae3ab3bd0248e8d426b50d82f24730c46a464ff52ba25a04e623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Continuity (mathematics)</topic><topic>Differential equations</topic><topic>Existence theorems</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary differential equations</topic><topic>Periodic functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Han, Xiaoling</creatorcontrib><creatorcontrib>Yang, Hujun</creatorcontrib><collection>CrossRef</collection><jtitle>Monatshefte für Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Han, Xiaoling</au><au>Yang, Hujun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations</atitle><jtitle>Monatshefte für Mathematik</jtitle><stitle>Monatsh Math</stitle><date>2020-12-01</date><risdate>2020</risdate><volume>193</volume><issue>4</issue><spage>829</spage><epage>843</epage><pages>829-843</pages><issn>0026-9255</issn><eissn>1436-5081</eissn><abstract>In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations
x
′
′
+
α
x
′
+
a
(
t
)
x
n
-
b
(
t
)
x
n
+
1
+
c
(
t
)
x
n
+
2
=
0
,
where
α
∈
R
is a constant,
n
is a finite positive integer, and
a
(
t
),
b
(
t
),
c
(
t
) are continuous periodic functions. By using Mawhin’s continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations.</abstract><cop>Vienna</cop><pub>Springer Vienna</pub><doi>10.1007/s00605-020-01465-w</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0026-9255 |
| ispartof | Monatshefte für Mathematik, 2020-12, Vol.193 (4), p.829-843 |
| issn | 0026-9255 1436-5081 |
| language | eng |
| recordid | cdi_proquest_journals_2450417232 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Continuity (mathematics) Differential equations Existence theorems Mathematical analysis Mathematics Mathematics and Statistics Ordinary differential equations Periodic functions |
| title | Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-20T19%3A18%3A55IST&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=Existence%20and%20multiplicity%20of%20periodic%20solutions%20for%20a%20class%20of%20second-order%20ordinary%20differential%20equations&rft.jtitle=Monatshefte%20f%C3%BCr%20Mathematik&rft.au=Han,%20Xiaoling&rft.date=2020-12-01&rft.volume=193&rft.issue=4&rft.spage=829&rft.epage=843&rft.pages=829-843&rft.issn=0026-9255&rft.eissn=1436-5081&rft_id=info:doi/10.1007/s00605-020-01465-w&rft_dat=%3Cproquest_cross%3E2450417232%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2450417232&rft_id=info:pmid/&rfr_iscdi=true |