On the elliptic problems with critical weighted Sobolev–Hardy exponents
Let Ω ⊂ R N be a smooth bounded domain such that 0 ∈ Ω , N ≥ 3 . In this paper, we deal with the conditions that ensure the existence of nontrivial solutions for the elliptic equation − div ( | x | − 2 a ∇ u ) − μ u | x | 2 ( 1 + a ) = | u | p − 2 | x | b p u + λ u with Dirichlet boundary condition,...
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| Veröffentlicht in: | Nonlinear analysis 2007-03, Vol.66 (5), p.1037-1050 |
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| container_title | Nonlinear analysis |
| container_volume | 66 |
| creator | Kang, Dongsheng |
| description | Let
Ω
⊂
R
N
be a smooth bounded domain such that
0
∈
Ω
,
N
≥
3
. In this paper, we deal with the conditions that ensure the existence of nontrivial solutions for the elliptic equation
−
div
(
|
x
|
−
2
a
∇
u
)
−
μ
u
|
x
|
2
(
1
+
a
)
=
|
u
|
p
−
2
|
x
|
b
p
u
+
λ
u
with Dirichlet boundary condition, which involving the Caffarelli–Kohn–Nirenberg inequalities. The results depend crucially on the parameters
a
,
b
,
λ
and
μ
. |
| doi_str_mv | 10.1016/j.na.2006.01.003 |
| format | Article |
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Ω
⊂
R
N
be a smooth bounded domain such that
0
∈
Ω
,
N
≥
3
. In this paper, we deal with the conditions that ensure the existence of nontrivial solutions for the elliptic equation
−
div
(
|
x
|
−
2
a
∇
u
)
−
μ
u
|
x
|
2
(
1
+
a
)
=
|
u
|
p
−
2
|
x
|
b
p
u
+
λ
u
with Dirichlet boundary condition, which involving the Caffarelli–Kohn–Nirenberg inequalities. The results depend crucially on the parameters
a
,
b
,
λ
and
μ
.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2006.01.003</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Caffarelli–Kohn–Nirenberg inequality ; Elliptic equation ; Exact sciences and technology ; Mathematical analysis ; Mathematics ; Nontrivial solution ; Partial differential equations ; Sciences and techniques of general use ; Variational method</subject><ispartof>Nonlinear analysis, 2007-03, Vol.66 (5), p.1037-1050</ispartof><rights>2006 Elsevier Ltd</rights><rights>2007 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-f977abbfc9bfb510c5b79c59b5418400cefff3eb438270bf1d105ce817c93c0c3</citedby><cites>FETCH-LOGICAL-c355t-f977abbfc9bfb510c5b79c59b5418400cefff3eb438270bf1d105ce817c93c0c3</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.2006.01.003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18437048$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Kang, Dongsheng</creatorcontrib><title>On the elliptic problems with critical weighted Sobolev–Hardy exponents</title><title>Nonlinear analysis</title><description>Let
Ω
⊂
R
N
be a smooth bounded domain such that
0
∈
Ω
,
N
≥
3
. In this paper, we deal with the conditions that ensure the existence of nontrivial solutions for the elliptic equation
−
div
(
|
x
|
−
2
a
∇
u
)
−
μ
u
|
x
|
2
(
1
+
a
)
=
|
u
|
p
−
2
|
x
|
b
p
u
+
λ
u
with Dirichlet boundary condition, which involving the Caffarelli–Kohn–Nirenberg inequalities. The results depend crucially on the parameters
a
,
b
,
λ
and
μ
.</description><subject>Caffarelli–Kohn–Nirenberg inequality</subject><subject>Elliptic equation</subject><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Nontrivial solution</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Variational method</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp1kM1O5DAQhK0VK-3wc-eYC9wS2nEcJ9wQ4k8aaQ6w0t4su9NmPMokgx0YuPEO-4b7JGs0SJw4tdT6qrq6GDvmUHDg9dmqGExRAtQF8AJA_GAz3iiRy5LLPTYDUZe5rOo_v9h-jCsA4ErUM3a3GLJpSRn1vd9MHrNNGG1P65ht_bTMMPi0NH22Jf-4nKjL7kc79vTy7_3vrQndW0avm3GgYYqH7KczfaSjz3nAfl9fPVze5vPFzd3lxTxHIeWUu1YpY63D1jorOaC0qkXZWlnxpgJAcs4JspVoSgXW8Y6DRGq4wlYgoDhgpzvflPTpmeKk1z5iym8GGp-jLttKCq54AmEHYhhjDOT0Jvi1CW-ag_7oTK_0YPRHZxq4Tp0lycmnt4npaxfMgD5-6ZpKKKiaxJ3vOEqPvngKOqKnAanzgXDS3ei_P_If_XeCYg</recordid><startdate>20070301</startdate><enddate>20070301</enddate><creator>Kang, Dongsheng</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>20070301</creationdate><title>On the elliptic problems with critical weighted Sobolev–Hardy exponents</title><author>Kang, Dongsheng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-f977abbfc9bfb510c5b79c59b5418400cefff3eb438270bf1d105ce817c93c0c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Caffarelli–Kohn–Nirenberg inequality</topic><topic>Elliptic equation</topic><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Nontrivial solution</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Variational method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kang, Dongsheng</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>Kang, Dongsheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the elliptic problems with critical weighted Sobolev–Hardy exponents</atitle><jtitle>Nonlinear analysis</jtitle><date>2007-03-01</date><risdate>2007</risdate><volume>66</volume><issue>5</issue><spage>1037</spage><epage>1050</epage><pages>1037-1050</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>Let
Ω
⊂
R
N
be a smooth bounded domain such that
0
∈
Ω
,
N
≥
3
. In this paper, we deal with the conditions that ensure the existence of nontrivial solutions for the elliptic equation
−
div
(
|
x
|
−
2
a
∇
u
)
−
μ
u
|
x
|
2
(
1
+
a
)
=
|
u
|
p
−
2
|
x
|
b
p
u
+
λ
u
with Dirichlet boundary condition, which involving the Caffarelli–Kohn–Nirenberg inequalities. The results depend crucially on the parameters
a
,
b
,
λ
and
μ
.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2006.01.003</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2007-03, Vol.66 (5), p.1037-1050 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_29453171 |
| source | Elsevier ScienceDirect Journals |
| subjects | Caffarelli–Kohn–Nirenberg inequality Elliptic equation Exact sciences and technology Mathematical analysis Mathematics Nontrivial solution Partial differential equations Sciences and techniques of general use Variational method |
| title | On the elliptic problems with critical weighted Sobolev–Hardy exponents |
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