On a p -Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem
In this paper, we show the existence of infinite solutions to the Kirchhoff type quasilinear elliptic equation [ M ( ∫ Ω ( ∣ ∇ u ∣ p + λ ( x ) ∣ u ∣ p ) d x ) ] p − 1 ( − Δ p u + λ ( x ) ∣ u ∣ p − 2 u ) = f ( x , u ) in a smooth bounded domain Ω ⊂ R N with nonlinear boundary condition ∣ ∇ u ∣ p − 2...
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| Veröffentlicht in: | Nonlinear analysis 2010, Vol.72 (1), p.302-308 |
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| container_title | Nonlinear analysis |
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| creator | Liu, Duchao |
| description | In this paper, we show the existence of infinite solutions to the Kirchhoff type quasilinear elliptic equation
[
M
(
∫
Ω
(
∣
∇
u
∣
p
+
λ
(
x
)
∣
u
∣
p
)
d
x
)
]
p
−
1
(
−
Δ
p
u
+
λ
(
x
)
∣
u
∣
p
−
2
u
)
=
f
(
x
,
u
)
in a smooth bounded domain
Ω
⊂
R
N
with nonlinear boundary condition
∣
∇
u
∣
p
−
2
∂
u
∂
ν
=
η
∣
u
∣
p
−
2
on
∂
Ω
. The method we used here is based on “Fountain Theorem” and “Dual Fountain Theorem”. |
| doi_str_mv | 10.1016/j.na.2009.06.052 |
| format | Article |
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M
(
∫
Ω
(
∣
∇
u
∣
p
+
λ
(
x
)
∣
u
∣
p
)
d
x
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λ
(
x
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∣
u
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−
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=
f
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x
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in a smooth bounded domain
Ω
⊂
R
N
with nonlinear boundary condition
∣
∇
u
∣
p
−
2
∂
u
∂
ν
=
η
∣
u
∣
p
−
2
on
∂
Ω
. The method we used here is based on “Fountain Theorem” and “Dual Fountain Theorem”.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2009.06.052</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>[formula omitted]-Kirchhoff problem ; Critical points ; Dual Fountain Theorem ; Exact sciences and technology ; Fountain Theorem ; Mathematical analysis ; Mathematics ; Partial differential equations ; Sciences and techniques of general use</subject><ispartof>Nonlinear analysis, 2010, Vol.72 (1), p.302-308</ispartof><rights>2009 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2009.06.052$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,4024,27923,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22272405$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Duchao</creatorcontrib><title>On a p -Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem</title><title>Nonlinear analysis</title><description>In this paper, we show the existence of infinite solutions to the Kirchhoff type quasilinear elliptic equation
[
M
(
∫
Ω
(
∣
∇
u
∣
p
+
λ
(
x
)
∣
u
∣
p
)
d
x
)
]
p
−
1
(
−
Δ
p
u
+
λ
(
x
)
∣
u
∣
p
−
2
u
)
=
f
(
x
,
u
)
in a smooth bounded domain
Ω
⊂
R
N
with nonlinear boundary condition
∣
∇
u
∣
p
−
2
∂
u
∂
ν
=
η
∣
u
∣
p
−
2
on
∂
Ω
. The method we used here is based on “Fountain Theorem” and “Dual Fountain Theorem”.</description><subject>[formula omitted]-Kirchhoff problem</subject><subject>Critical points</subject><subject>Dual Fountain Theorem</subject><subject>Exact sciences and technology</subject><subject>Fountain Theorem</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNplkD1PwzAURS0EEqWwM3qBLcEfsZ2woUKholKXIrFZL_GL6ip12jhB4t-Tqt2Y3nCPru47hNxzlnLG9dM2DZAKxoqU6ZQpcUEmPDcyUYKrSzJhUotEZfr7mtzEuGWMcSP1hCxWgQLd0-TTd9Vm09Y1xcMAvW8D_fFA5-0QevCBrjfYdrijEBx9HaD5l9ySqxqaiHfnOyVf87f17CNZrt4Xs5dlgkKbPkGtBUPloBK8VGVZSy6dYWXNC6xdLp10hciFyQoFaLQGHL_IdOEUL02RZXJKHk-9-649DBh7u_OxwqaBgO0QrdRZYXLBRvDhDEKsoKk7CJWPdt_5HXS_VghhRMbUyD2fOBxX_3jsbKw8hgqd77DqrWu95cweLdutDWCPli3TdrQs_wCUzG-c</recordid><startdate>2010</startdate><enddate>2010</enddate><creator>Liu, Duchao</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2010</creationdate><title>On a p -Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem</title><author>Liu, Duchao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-e267t-e6620e5dac21b5bbf313d70bf19efd83d3d92827495ae766ae873469d51b79443</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>[formula omitted]-Kirchhoff problem</topic><topic>Critical points</topic><topic>Dual Fountain Theorem</topic><topic>Exact sciences and technology</topic><topic>Fountain Theorem</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Duchao</creatorcontrib><collection>Pascal-Francis</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Duchao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a p -Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem</atitle><jtitle>Nonlinear analysis</jtitle><date>2010</date><risdate>2010</risdate><volume>72</volume><issue>1</issue><spage>302</spage><epage>308</epage><pages>302-308</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>In this paper, we show the existence of infinite solutions to the Kirchhoff type quasilinear elliptic equation
[
M
(
∫
Ω
(
∣
∇
u
∣
p
+
λ
(
x
)
∣
u
∣
p
)
d
x
)
]
p
−
1
(
−
Δ
p
u
+
λ
(
x
)
∣
u
∣
p
−
2
u
)
=
f
(
x
,
u
)
in a smooth bounded domain
Ω
⊂
R
N
with nonlinear boundary condition
∣
∇
u
∣
p
−
2
∂
u
∂
ν
=
η
∣
u
∣
p
−
2
on
∂
Ω
. The method we used here is based on “Fountain Theorem” and “Dual Fountain Theorem”.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2009.06.052</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2010, Vol.72 (1), p.302-308 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_36497820 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | [formula omitted]-Kirchhoff problem Critical points Dual Fountain Theorem Exact sciences and technology Fountain Theorem Mathematical analysis Mathematics Partial differential equations Sciences and techniques of general use |
| title | On a p -Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem |
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