Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type
This paper deals with the multiplicity of weak solutions in W 0 1 ( Ω ) to a class of nonuniformly elliptic equations of the form − div ( a ( x , ∇ u ) ) = h ( x ) | u | r − 1 u + g ( x ) | u | s − 1 u in a bounded domain Ω of R N . Here a satisfies | a ( x , ξ ) | ≦ c 0 ( h 0 ( x ) + h 1 ( x ) | ξ...
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| Veröffentlicht in: | Nonlinear analysis 2009-02, Vol.70 (4), p.1536-1546 |
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| container_title | Nonlinear analysis |
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| creator | Quoc Toan, Hoang Ngô, Quô ́c-Anh |
| description | This paper deals with the multiplicity of weak solutions in
W
0
1
(
Ω
)
to a class of nonuniformly elliptic equations of the form
−
div
(
a
(
x
,
∇
u
)
)
=
h
(
x
)
|
u
|
r
−
1
u
+
g
(
x
)
|
u
|
s
−
1
u
in a bounded domain
Ω
of
R
N
. Here
a
satisfies
|
a
(
x
,
ξ
)
|
≦
c
0
(
h
0
(
x
)
+
h
1
(
x
)
|
ξ
|
p
−
1
)
for all
ξ
∈
R
N
, a.e.
x
∈
Ω
,
h
0
∈
L
p
p
−
1
(
Ω
)
,
h
1
∈
L
loc
1
(
Ω
)
,
h
1
(
x
)
≧
1
for a.e.
x
in
Ω
,
1
<
r
<
p
−
1
<
s
<
(
N
p
−
N
+
p
)
/
(
N
−
p
)
. |
| doi_str_mv | 10.1016/j.na.2008.02.033 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_36009176</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X08000990</els_id><sourcerecordid>36009176</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-a1028a46a702a067b9529e170b72561ca2727897f2ccc219ed96ff0e39853a833</originalsourceid><addsrcrecordid>eNp1kL1LBDEQxYMoeH70lmm023WSmGTXTsQvOLFRsAtzuSzkzCVrsqvcf-8eJ3ZWAzO_92bmEXLGoGbA1OWqjlhzgKYGXoMQe2TGGi0qyZncJzMQilfySr0fkqNSVgDAtFAzsngew-D74K0fNjR19NvhBy0pjINPsdAuZYrUBixlO40pjtFPzXXYUBeC7wdvqfsccYdPSE-rOfYBrcdIh03vTshBh6G40996TN7u715vH6v5y8PT7c28skLKoUIGvMErhRo4gtKLVvLWMQ0LzaViFrnmuml1x621nLVu2aquAyfaRgpshDgmFzvfPqfP0ZXBrH2x05EYXRqLEQqgZVpNIOxAm1Mp2XWmz36NeWMYmG2YZmUimm2YBriZwpwk57_eWCyGLmO0vvzpOAPNuZITd73j3PTol3fZFOtdtG7ps7ODWSb__5Ifc3WJAA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>36009176</pqid></control><display><type>article</type><title>Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type</title><source>Elsevier ScienceDirect Journals Complete</source><creator>Quoc Toan, Hoang ; Ngô, Quô ́c-Anh</creator><creatorcontrib>Quoc Toan, Hoang ; Ngô, Quô ́c-Anh</creatorcontrib><description>This paper deals with the multiplicity of weak solutions in
W
0
1
(
Ω
)
to a class of nonuniformly elliptic equations of the form
−
div
(
a
(
x
,
∇
u
)
)
=
h
(
x
)
|
u
|
r
−
1
u
+
g
(
x
)
|
u
|
s
−
1
u
in a bounded domain
Ω
of
R
N
. Here
a
satisfies
|
a
(
x
,
ξ
)
|
≦
c
0
(
h
0
(
x
)
+
h
1
(
x
)
|
ξ
|
p
−
1
)
for all
ξ
∈
R
N
, a.e.
x
∈
Ω
,
h
0
∈
L
p
p
−
1
(
Ω
)
,
h
1
∈
L
loc
1
(
Ω
)
,
h
1
(
x
)
≧
1
for a.e.
x
in
Ω
,
1
<
r
<
p
−
1
<
s
<
(
N
p
−
N
+
p
)
/
(
N
−
p
)
.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2008.02.033</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>[formula omitted]-Laplacian ; Algebra ; Commutative rings and algebras ; Exact sciences and technology ; Mathematical analysis ; Mathematics ; Multiplicity ; Nonuniform elliptic equations ; Partial differential equations ; Sciences and techniques of general use</subject><ispartof>Nonlinear analysis, 2009-02, Vol.70 (4), p.1536-1546</ispartof><rights>2008 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-a1028a46a702a067b9529e170b72561ca2727897f2ccc219ed96ff0e39853a833</citedby><cites>FETCH-LOGICAL-c355t-a1028a46a702a067b9529e170b72561ca2727897f2ccc219ed96ff0e39853a833</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2008.02.033$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21072265$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Quoc Toan, Hoang</creatorcontrib><creatorcontrib>Ngô, Quô ́c-Anh</creatorcontrib><title>Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type</title><title>Nonlinear analysis</title><description>This paper deals with the multiplicity of weak solutions in
W
0
1
(
Ω
)
to a class of nonuniformly elliptic equations of the form
−
div
(
a
(
x
,
∇
u
)
)
=
h
(
x
)
|
u
|
r
−
1
u
+
g
(
x
)
|
u
|
s
−
1
u
in a bounded domain
Ω
of
R
N
. Here
a
satisfies
|
a
(
x
,
ξ
)
|
≦
c
0
(
h
0
(
x
)
+
h
1
(
x
)
|
ξ
|
p
−
1
)
for all
ξ
∈
R
N
, a.e.
x
∈
Ω
,
h
0
∈
L
p
p
−
1
(
Ω
)
,
h
1
∈
L
loc
1
(
Ω
)
,
h
1
(
x
)
≧
1
for a.e.
x
in
Ω
,
1
<
r
<
p
−
1
<
s
<
(
N
p
−
N
+
p
)
/
(
N
−
p
)
.</description><subject>[formula omitted]-Laplacian</subject><subject>Algebra</subject><subject>Commutative rings and algebras</subject><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Multiplicity</subject><subject>Nonuniform elliptic equations</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>2009</creationdate><recordtype>article</recordtype><recordid>eNp1kL1LBDEQxYMoeH70lmm023WSmGTXTsQvOLFRsAtzuSzkzCVrsqvcf-8eJ3ZWAzO_92bmEXLGoGbA1OWqjlhzgKYGXoMQe2TGGi0qyZncJzMQilfySr0fkqNSVgDAtFAzsngew-D74K0fNjR19NvhBy0pjINPsdAuZYrUBixlO40pjtFPzXXYUBeC7wdvqfsccYdPSE-rOfYBrcdIh03vTshBh6G40996TN7u715vH6v5y8PT7c28skLKoUIGvMErhRo4gtKLVvLWMQ0LzaViFrnmuml1x621nLVu2aquAyfaRgpshDgmFzvfPqfP0ZXBrH2x05EYXRqLEQqgZVpNIOxAm1Mp2XWmz36NeWMYmG2YZmUimm2YBriZwpwk57_eWCyGLmO0vvzpOAPNuZITd73j3PTol3fZFOtdtG7ps7ODWSb__5Ifc3WJAA</recordid><startdate>20090215</startdate><enddate>20090215</enddate><creator>Quoc Toan, Hoang</creator><creator>Ngô, Quô ́c-Anh</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20090215</creationdate><title>Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type</title><author>Quoc Toan, Hoang ; Ngô, Quô ́c-Anh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-a1028a46a702a067b9529e170b72561ca2727897f2ccc219ed96ff0e39853a833</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>[formula omitted]-Laplacian</topic><topic>Algebra</topic><topic>Commutative rings and algebras</topic><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Multiplicity</topic><topic>Nonuniform elliptic equations</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Quoc Toan, Hoang</creatorcontrib><creatorcontrib>Ngô, Quô ́c-Anh</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</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>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>Quoc Toan, Hoang</au><au>Ngô, Quô ́c-Anh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type</atitle><jtitle>Nonlinear analysis</jtitle><date>2009-02-15</date><risdate>2009</risdate><volume>70</volume><issue>4</issue><spage>1536</spage><epage>1546</epage><pages>1536-1546</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>This paper deals with the multiplicity of weak solutions in
W
0
1
(
Ω
)
to a class of nonuniformly elliptic equations of the form
−
div
(
a
(
x
,
∇
u
)
)
=
h
(
x
)
|
u
|
r
−
1
u
+
g
(
x
)
|
u
|
s
−
1
u
in a bounded domain
Ω
of
R
N
. Here
a
satisfies
|
a
(
x
,
ξ
)
|
≦
c
0
(
h
0
(
x
)
+
h
1
(
x
)
|
ξ
|
p
−
1
)
for all
ξ
∈
R
N
, a.e.
x
∈
Ω
,
h
0
∈
L
p
p
−
1
(
Ω
)
,
h
1
∈
L
loc
1
(
Ω
)
,
h
1
(
x
)
≧
1
for a.e.
x
in
Ω
,
1
<
r
<
p
−
1
<
s
<
(
N
p
−
N
+
p
)
/
(
N
−
p
)
.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2008.02.033</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2009-02, Vol.70 (4), p.1536-1546 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_36009176 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | [formula omitted]-Laplacian Algebra Commutative rings and algebras Exact sciences and technology Mathematical analysis Mathematics Multiplicity Nonuniform elliptic equations Partial differential equations Sciences and techniques of general use |
| title | Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type |
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