ON SOME SEMILINEAR ELLIPTIC PROBLEMS WITH SINGULAR POTENTIALS INVOLVING SYMMETRY
This paper deals with the existence and multiplicity of solutions for a class of semilinear elliptic problems of the form { − Δ u = u = μ | x | 2 u + f ( x , u ) 0 in on Ω , ∂ Ω , where Ω = Ω1× Ω2⊂ ℝ N (N≧ 5) is a bounded domain having cylindrical symmetry, Ω1⊂ ℝ m is a bounded regular domain and Ω2...
Gespeichert in:
| Veröffentlicht in: | Taiwanese journal of mathematics 2011-04, Vol.15 (2), p.623-631 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 631 |
|---|---|
| container_issue | 2 |
| container_start_page | 623 |
| container_title | Taiwanese journal of mathematics |
| container_volume | 15 |
| creator | Toan, Hoang Quoc Chung, Nguyen Thanh |
| description | This paper deals with the existence and multiplicity of solutions for a class of semilinear elliptic problems of the form
{
−
Δ
u
=
u
=
μ
|
x
|
2
u
+
f
(
x
,
u
)
0
in
on
Ω
,
∂
Ω
,
where Ω = Ω1× Ω2⊂ ℝ
N
(N≧ 5) is a bounded domain having cylindrical symmetry, Ω1⊂ ℝ
m
is a bounded regular domain and Ω2is ak-dimensional ball of radiusR, centered in the origin andm+k=N, andm≧ 2,k≧ 3,
0
≦
μ
<
μ
*
=
(
N
−
2
2
)
2
. The proofs rely essentially on the critical point theory tools combined with the Hardy inequality.
2000Mathematics Subject Classification: 35J65, 35J20.
Key words and phrases: Semilinear elliptic problems, Singular potentials, Symmetry, Ekeland's variational principle, Mountain pass theorem. |
| doi_str_mv | 10.11650/twjm/1500406225 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_11650_twjm_1500406225</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>taiwjmath.15.2.623</jstor_id><sourcerecordid>taiwjmath.15.2.623</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-a4ab345b18e4031f89e22e2efaa23a4dbb39ca780ad3cd156a647c73fb5bb9843</originalsourceid><addsrcrecordid>eNpFkDtPwzAYRS0EEqWwM3pjCrU_P-KOpTKtJeehJi3qZNlpIlpRFSWREP-eQBFMd7jn3uEgdE_JI6VSkEn_cThOqCCEEwkgLtAIAHgklaCXaEQJxJHgKr5GN113IASUpHKE8izFRZZoXOjEWJPq2Qpra01emjnOV9mT1UmBX0y5xIVJF2s79HlW6rQ0M1tgk24yuxkKXGyTRJer7S26avxbV9_95hitn3U5X0Y2W5j5zEYVxKSPPPeBcRGoqjlhtFHTGqCGuvEemOe7ENi08rEifseqHRXSSx5XMWuCCGGqOBsjcv6t2lPXtXXj3tv90befjhL3Y8R9G3H_RobJw3ly6PpT-8f3fj-Avn8dWAdOAmNfWmBc1g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>ON SOME SEMILINEAR ELLIPTIC PROBLEMS WITH SINGULAR POTENTIALS INVOLVING SYMMETRY</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>JSTOR Mathematics & Statistics</source><source>Jstor Complete Legacy</source><source>Project Euclid Open Access</source><source>Project Euclid Complete</source><creator>Toan, Hoang Quoc ; Chung, Nguyen Thanh</creator><creatorcontrib>Toan, Hoang Quoc ; Chung, Nguyen Thanh</creatorcontrib><description>This paper deals with the existence and multiplicity of solutions for a class of semilinear elliptic problems of the form
{
−
Δ
u
=
u
=
μ
|
x
|
2
u
+
f
(
x
,
u
)
0
in
on
Ω
,
∂
Ω
,
where Ω = Ω1× Ω2⊂ ℝ
N
(N≧ 5) is a bounded domain having cylindrical symmetry, Ω1⊂ ℝ
m
is a bounded regular domain and Ω2is ak-dimensional ball of radiusR, centered in the origin andm+k=N, andm≧ 2,k≧ 3,
0
≦
μ
<
μ
*
=
(
N
−
2
2
)
2
. The proofs rely essentially on the critical point theory tools combined with the Hardy inequality.
2000Mathematics Subject Classification: 35J65, 35J20.
Key words and phrases: Semilinear elliptic problems, Singular potentials, Symmetry, Ekeland's variational principle, Mountain pass theorem.</description><identifier>ISSN: 1027-5487</identifier><identifier>EISSN: 2224-6851</identifier><identifier>DOI: 10.11650/twjm/1500406225</identifier><language>eng</language><publisher>Mathematical Society of the Republic of China</publisher><subject>Mathematical theorems ; Mountain passes</subject><ispartof>Taiwanese journal of mathematics, 2011-04, Vol.15 (2), p.623-631</ispartof><rights>2011 Mathematical Society of the Republic of China</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-a4ab345b18e4031f89e22e2efaa23a4dbb39ca780ad3cd156a647c73fb5bb9843</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/taiwjmath.15.2.623$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/taiwjmath.15.2.623$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,778,782,801,830,27907,27908,58000,58004,58233,58237</link.rule.ids></links><search><creatorcontrib>Toan, Hoang Quoc</creatorcontrib><creatorcontrib>Chung, Nguyen Thanh</creatorcontrib><title>ON SOME SEMILINEAR ELLIPTIC PROBLEMS WITH SINGULAR POTENTIALS INVOLVING SYMMETRY</title><title>Taiwanese journal of mathematics</title><description>This paper deals with the existence and multiplicity of solutions for a class of semilinear elliptic problems of the form
{
−
Δ
u
=
u
=
μ
|
x
|
2
u
+
f
(
x
,
u
)
0
in
on
Ω
,
∂
Ω
,
where Ω = Ω1× Ω2⊂ ℝ
N
(N≧ 5) is a bounded domain having cylindrical symmetry, Ω1⊂ ℝ
m
is a bounded regular domain and Ω2is ak-dimensional ball of radiusR, centered in the origin andm+k=N, andm≧ 2,k≧ 3,
0
≦
μ
<
μ
*
=
(
N
−
2
2
)
2
. The proofs rely essentially on the critical point theory tools combined with the Hardy inequality.
2000Mathematics Subject Classification: 35J65, 35J20.
Key words and phrases: Semilinear elliptic problems, Singular potentials, Symmetry, Ekeland's variational principle, Mountain pass theorem.</description><subject>Mathematical theorems</subject><subject>Mountain passes</subject><issn>1027-5487</issn><issn>2224-6851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNpFkDtPwzAYRS0EEqWwM3pjCrU_P-KOpTKtJeehJi3qZNlpIlpRFSWREP-eQBFMd7jn3uEgdE_JI6VSkEn_cThOqCCEEwkgLtAIAHgklaCXaEQJxJHgKr5GN113IASUpHKE8izFRZZoXOjEWJPq2Qpra01emjnOV9mT1UmBX0y5xIVJF2s79HlW6rQ0M1tgk24yuxkKXGyTRJer7S26avxbV9_95hitn3U5X0Y2W5j5zEYVxKSPPPeBcRGoqjlhtFHTGqCGuvEemOe7ENi08rEifseqHRXSSx5XMWuCCGGqOBsjcv6t2lPXtXXj3tv90befjhL3Y8R9G3H_RobJw3ly6PpT-8f3fj-Avn8dWAdOAmNfWmBc1g</recordid><startdate>20110401</startdate><enddate>20110401</enddate><creator>Toan, Hoang Quoc</creator><creator>Chung, Nguyen Thanh</creator><general>Mathematical Society of the Republic of China</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20110401</creationdate><title>ON SOME SEMILINEAR ELLIPTIC PROBLEMS WITH SINGULAR POTENTIALS INVOLVING SYMMETRY</title><author>Toan, Hoang Quoc ; Chung, Nguyen Thanh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-a4ab345b18e4031f89e22e2efaa23a4dbb39ca780ad3cd156a647c73fb5bb9843</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematical theorems</topic><topic>Mountain passes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Toan, Hoang Quoc</creatorcontrib><creatorcontrib>Chung, Nguyen Thanh</creatorcontrib><collection>CrossRef</collection><jtitle>Taiwanese journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Toan, Hoang Quoc</au><au>Chung, Nguyen Thanh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON SOME SEMILINEAR ELLIPTIC PROBLEMS WITH SINGULAR POTENTIALS INVOLVING SYMMETRY</atitle><jtitle>Taiwanese journal of mathematics</jtitle><date>2011-04-01</date><risdate>2011</risdate><volume>15</volume><issue>2</issue><spage>623</spage><epage>631</epage><pages>623-631</pages><issn>1027-5487</issn><eissn>2224-6851</eissn><abstract>This paper deals with the existence and multiplicity of solutions for a class of semilinear elliptic problems of the form
{
−
Δ
u
=
u
=
μ
|
x
|
2
u
+
f
(
x
,
u
)
0
in
on
Ω
,
∂
Ω
,
where Ω = Ω1× Ω2⊂ ℝ
N
(N≧ 5) is a bounded domain having cylindrical symmetry, Ω1⊂ ℝ
m
is a bounded regular domain and Ω2is ak-dimensional ball of radiusR, centered in the origin andm+k=N, andm≧ 2,k≧ 3,
0
≦
μ
<
μ
*
=
(
N
−
2
2
)
2
. The proofs rely essentially on the critical point theory tools combined with the Hardy inequality.
2000Mathematics Subject Classification: 35J65, 35J20.
Key words and phrases: Semilinear elliptic problems, Singular potentials, Symmetry, Ekeland's variational principle, Mountain pass theorem.</abstract><pub>Mathematical Society of the Republic of China</pub><doi>10.11650/twjm/1500406225</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1027-5487 |
| ispartof | Taiwanese journal of mathematics, 2011-04, Vol.15 (2), p.623-631 |
| issn | 1027-5487 2224-6851 |
| language | eng |
| recordid | cdi_crossref_primary_10_11650_twjm_1500406225 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Project Euclid Open Access; Project Euclid Complete |
| subjects | Mathematical theorems Mountain passes |
| title | ON SOME SEMILINEAR ELLIPTIC PROBLEMS WITH SINGULAR POTENTIALS INVOLVING SYMMETRY |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T22%3A45%3A18IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=ON%20SOME%20SEMILINEAR%20ELLIPTIC%20PROBLEMS%20WITH%20SINGULAR%20POTENTIALS%20INVOLVING%20SYMMETRY&rft.jtitle=Taiwanese%20journal%20of%20mathematics&rft.au=Toan,%20Hoang%20Quoc&rft.date=2011-04-01&rft.volume=15&rft.issue=2&rft.spage=623&rft.epage=631&rft.pages=623-631&rft.issn=1027-5487&rft.eissn=2224-6851&rft_id=info:doi/10.11650/twjm/1500406225&rft_dat=%3Cjstor_cross%3Etaiwjmath.15.2.623%3C/jstor_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=taiwjmath.15.2.623&rfr_iscdi=true |