Multiple solutions for a class of N-Kirchhoff type equations via variational methods
In this article, we consider the following N -Kirchhoff type problem - M ∫ Ω | ∇ u | N d x Δ N u = λ f ( x , u ) + μ g ( x , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded smooth domain of R N , N ≥ 2 , M : R 0 + → R is a continuous function, Δ N u = div ( | ∇ u | N - 2 ∇ u ) , f , g : Ω × R → R are...
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| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2015-03, Vol.109 (1), p.247-256 |
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| container_title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas |
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| creator | Chung, Nguyen Thanh Toan, Hoang Quoc |
| description | In this article, we consider the following
N
-Kirchhoff type problem
-
M
∫
Ω
|
∇
u
|
N
d
x
Δ
N
u
=
λ
f
(
x
,
u
)
+
μ
g
(
x
,
u
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded smooth domain of
R
N
,
N
≥
2
,
M
:
R
0
+
→
R
is a continuous function,
Δ
N
u
=
div
(
|
∇
u
|
N
-
2
∇
u
)
,
f
,
g
:
Ω
×
R
→
R
are two Carathéodory functions and
λ
,
μ
are positive parameters. Using variational method, we show the existence of at least three weak solutions for the problem. |
| doi_str_mv | 10.1007/s13398-014-0177-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_1818719033</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>4179784741</sourcerecordid><originalsourceid>FETCH-LOGICAL-p226t-3f17c3293f15594ae9073ef2b31ce283625901d199325d0e411cdb0fd82e25d43</originalsourceid><addsrcrecordid>eNpNkEtLAzEQgIMoWGp_gLeA52gms2mSoxRfWPVSz0u6m9gta7NNdgv-e9OuBweGefAxDB8h18BvgXN1lwDRaMahyKkUwzMyAakMA8nl-anXTCHHSzJLactzIBSaqwlZvQ1t33Stoym0Q9-EXaI-RGpp1dqUaPD0nb02sdpsgve0_-kcdfvBjuShsfRgY3MabUu_Xb8JdboiF962yc3-6pR8Pj6sFs9s-fH0srhfsk6Iec_Qg6pQmFylNIV1hit0XqwRKic0zoU0HGowBoWsuSsAqnrNfa2Fy4sCp-RmvNvFsB9c6sttGGJ-JJWgQSswHDFTYqRSF5vdl4v_KF4eBZajwDILLI8CS8Rf8Exiow</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1818719033</pqid></control><display><type>article</type><title>Multiple solutions for a class of N-Kirchhoff type equations via variational methods</title><source>SpringerLink Journals - AutoHoldings</source><creator>Chung, Nguyen Thanh ; Toan, Hoang Quoc</creator><creatorcontrib>Chung, Nguyen Thanh ; Toan, Hoang Quoc</creatorcontrib><description>In this article, we consider the following
N
-Kirchhoff type problem
-
M
∫
Ω
|
∇
u
|
N
d
x
Δ
N
u
=
λ
f
(
x
,
u
)
+
μ
g
(
x
,
u
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded smooth domain of
R
N
,
N
≥
2
,
M
:
R
0
+
→
R
is a continuous function,
Δ
N
u
=
div
(
|
∇
u
|
N
-
2
∇
u
)
,
f
,
g
:
Ω
×
R
→
R
are two Carathéodory functions and
λ
,
μ
are positive parameters. Using variational method, we show the existence of at least three weak solutions for the problem.</description><identifier>ISSN: 1578-7303</identifier><identifier>EISSN: 1579-1505</identifier><identifier>DOI: 10.1007/s13398-014-0177-3</identifier><language>eng</language><publisher>Milan: Springer Milan</publisher><subject>Applications of Mathematics ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Original Paper ; Theoretical</subject><ispartof>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2015-03, Vol.109 (1), p.247-256</ispartof><rights>Springer-Verlag Italia 2014</rights><rights>Springer-Verlag Italia 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13398-014-0177-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13398-014-0177-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Chung, Nguyen Thanh</creatorcontrib><creatorcontrib>Toan, Hoang Quoc</creatorcontrib><title>Multiple solutions for a class of N-Kirchhoff type equations via variational methods</title><title>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</title><addtitle>RACSAM</addtitle><description>In this article, we consider the following
N
-Kirchhoff type problem
-
M
∫
Ω
|
∇
u
|
N
d
x
Δ
N
u
=
λ
f
(
x
,
u
)
+
μ
g
(
x
,
u
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded smooth domain of
R
N
,
N
≥
2
,
M
:
R
0
+
→
R
is a continuous function,
Δ
N
u
=
div
(
|
∇
u
|
N
-
2
∇
u
)
,
f
,
g
:
Ω
×
R
→
R
are two Carathéodory functions and
λ
,
μ
are positive parameters. Using variational method, we show the existence of at least three weak solutions for the problem.</description><subject>Applications of Mathematics</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Theoretical</subject><issn>1578-7303</issn><issn>1579-1505</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpNkEtLAzEQgIMoWGp_gLeA52gms2mSoxRfWPVSz0u6m9gta7NNdgv-e9OuBweGefAxDB8h18BvgXN1lwDRaMahyKkUwzMyAakMA8nl-anXTCHHSzJLactzIBSaqwlZvQ1t33Stoym0Q9-EXaI-RGpp1dqUaPD0nb02sdpsgve0_-kcdfvBjuShsfRgY3MabUu_Xb8JdboiF962yc3-6pR8Pj6sFs9s-fH0srhfsk6Iec_Qg6pQmFylNIV1hit0XqwRKic0zoU0HGowBoWsuSsAqnrNfa2Fy4sCp-RmvNvFsB9c6sttGGJ-JJWgQSswHDFTYqRSF5vdl4v_KF4eBZajwDILLI8CS8Rf8Exiow</recordid><startdate>20150301</startdate><enddate>20150301</enddate><creator>Chung, Nguyen Thanh</creator><creator>Toan, Hoang Quoc</creator><general>Springer Milan</general><general>Springer Nature B.V</general><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20150301</creationdate><title>Multiple solutions for a class of N-Kirchhoff type equations via variational methods</title><author>Chung, Nguyen Thanh ; Toan, Hoang Quoc</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p226t-3f17c3293f15594ae9073ef2b31ce283625901d199325d0e411cdb0fd82e25d43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Applications of Mathematics</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chung, Nguyen Thanh</creatorcontrib><creatorcontrib>Toan, Hoang Quoc</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</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>Engineering 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>Engineering Collection</collection><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chung, Nguyen Thanh</au><au>Toan, Hoang Quoc</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiple solutions for a class of N-Kirchhoff type equations via variational methods</atitle><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle><stitle>RACSAM</stitle><date>2015-03-01</date><risdate>2015</risdate><volume>109</volume><issue>1</issue><spage>247</spage><epage>256</epage><pages>247-256</pages><issn>1578-7303</issn><eissn>1579-1505</eissn><abstract>In this article, we consider the following
N
-Kirchhoff type problem
-
M
∫
Ω
|
∇
u
|
N
d
x
Δ
N
u
=
λ
f
(
x
,
u
)
+
μ
g
(
x
,
u
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded smooth domain of
R
N
,
N
≥
2
,
M
:
R
0
+
→
R
is a continuous function,
Δ
N
u
=
div
(
|
∇
u
|
N
-
2
∇
u
)
,
f
,
g
:
Ω
×
R
→
R
are two Carathéodory functions and
λ
,
μ
are positive parameters. Using variational method, we show the existence of at least three weak solutions for the problem.</abstract><cop>Milan</cop><pub>Springer Milan</pub><doi>10.1007/s13398-014-0177-3</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1578-7303 |
| ispartof | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2015-03, Vol.109 (1), p.247-256 |
| issn | 1578-7303 1579-1505 |
| language | eng |
| recordid | cdi_proquest_journals_1818719033 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical |
| title | Multiple solutions for a class of N-Kirchhoff type equations via variational methods |
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