Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains
This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that q c = n ( p − 1 ) / ( n − p ) is its critical exponent provided 2 n / ( n + 1 ) < p < n . Fu...
Gespeichert in:
| Veröffentlicht in: | Nonlinear analysis 2007-08, Vol.67 (3), p.901-916 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 916 |
|---|---|
| container_issue | 3 |
| container_start_page | 901 |
| container_title | Nonlinear analysis |
| container_volume | 67 |
| creator | Zeng, Xianzhong |
| description | This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that
q
c
=
n
(
p
−
1
)
/
(
n
−
p
)
is its critical exponent provided
2
n
/
(
n
+
1
)
<
p
<
n
. Furthermore, we prove that if
max
{
1
,
p
−
1
}
<
q
≤
q
c
, then every positive solution of the equations blows up in finite time; whereas for
q
>
q
c
, the equations admit the global positive solutions for some boundary value
f
(
x
)
and some initial data
u
0
(
x
)
. We also demonstrate that every positive solution of the equations blows up in finite time provided
n
≤
p
. |
| doi_str_mv | 10.1016/j.na.2006.06.048 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_29984410</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X06003646</els_id><sourcerecordid>29984410</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-dc6b9f4e284eea39350f764a7c04dc63ecb069a908bde0769a78781c43aad7ca3</originalsourceid><addsrcrecordid>eNp1kE1rGzEQhkVJoE7Se4-6tLd1pZVWq80thKQpGNJDA72JsXa2lVlLjmZtkn9fLTbpKTAwX8_MMC9jn6VYSiHNt80ywrIWwixn0_YDW0jbqqqpZXPGFkKZumq0-f2RXRBthBCyVWbB6O4l0ITRI4fY85givhXSwP-MaQ0j3yUKUzggpzTup5Ai8SFlPv1FjodTif-sVrAbwQeIHJ_3cORCSV4mzKHwfdpCiHTFzgcYCT-d_CV7ur_7dftQrR6__7i9WVVeNc1U9d6su0FjbTUiqE41YmiNhtYLXXoK_VqYDjph1z2KtoStba30WgH0rQd1yb4e9-5yet4jTW4byOM4QsS0J1d3ndVaigKKI-hzIso4uF0OW8ivTgo3q-s2LoKb1XWzaVtGvpx2A3kYhwzRB_o_V6S32prCXR85LI8eAmZHPszq9iGjn1yfwvtH_gGnQpG7</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>29984410</pqid></control><display><type>article</type><title>Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains</title><source>Access via ScienceDirect (Elsevier)</source><creator>Zeng, Xianzhong</creator><creatorcontrib>Zeng, Xianzhong</creatorcontrib><description>This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that
q
c
=
n
(
p
−
1
)
/
(
n
−
p
)
is its critical exponent provided
2
n
/
(
n
+
1
)
<
p
<
n
. Furthermore, we prove that if
max
{
1
,
p
−
1
}
<
q
≤
q
c
, then every positive solution of the equations blows up in finite time; whereas for
q
>
q
c
, the equations admit the global positive solutions for some boundary value
f
(
x
)
and some initial data
u
0
(
x
)
. We also demonstrate that every positive solution of the equations blows up in finite time provided
n
≤
p
.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2006.06.048</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Blow-up ; Critical exponent ; Exact sciences and technology ; Exterior domain ; Global analysis, analysis on manifolds ; Global existence ; Inhomogeneous boundary conditions ; Mathematical analysis ; Mathematics ; Partial differential equations ; Sciences and techniques of general use ; The evolution P-Laplacian equations ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinear analysis, 2007-08, Vol.67 (3), p.901-916</ispartof><rights>2006 Elsevier Ltd</rights><rights>2007 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-dc6b9f4e284eea39350f764a7c04dc63ecb069a908bde0769a78781c43aad7ca3</citedby><cites>FETCH-LOGICAL-c355t-dc6b9f4e284eea39350f764a7c04dc63ecb069a908bde0769a78781c43aad7ca3</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.2006.06.048$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18738486$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Zeng, Xianzhong</creatorcontrib><title>Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains</title><title>Nonlinear analysis</title><description>This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that
q
c
=
n
(
p
−
1
)
/
(
n
−
p
)
is its critical exponent provided
2
n
/
(
n
+
1
)
<
p
<
n
. Furthermore, we prove that if
max
{
1
,
p
−
1
}
<
q
≤
q
c
, then every positive solution of the equations blows up in finite time; whereas for
q
>
q
c
, the equations admit the global positive solutions for some boundary value
f
(
x
)
and some initial data
u
0
(
x
)
. We also demonstrate that every positive solution of the equations blows up in finite time provided
n
≤
p
.</description><subject>Blow-up</subject><subject>Critical exponent</subject><subject>Exact sciences and technology</subject><subject>Exterior domain</subject><subject>Global analysis, analysis on manifolds</subject><subject>Global existence</subject><subject>Inhomogeneous boundary conditions</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>The evolution P-Laplacian equations</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp1kE1rGzEQhkVJoE7Se4-6tLd1pZVWq80thKQpGNJDA72JsXa2lVlLjmZtkn9fLTbpKTAwX8_MMC9jn6VYSiHNt80ywrIWwixn0_YDW0jbqqqpZXPGFkKZumq0-f2RXRBthBCyVWbB6O4l0ITRI4fY85givhXSwP-MaQ0j3yUKUzggpzTup5Ai8SFlPv1FjodTif-sVrAbwQeIHJ_3cORCSV4mzKHwfdpCiHTFzgcYCT-d_CV7ur_7dftQrR6__7i9WVVeNc1U9d6su0FjbTUiqE41YmiNhtYLXXoK_VqYDjph1z2KtoStba30WgH0rQd1yb4e9-5yet4jTW4byOM4QsS0J1d3ndVaigKKI-hzIso4uF0OW8ivTgo3q-s2LoKb1XWzaVtGvpx2A3kYhwzRB_o_V6S32prCXR85LI8eAmZHPszq9iGjn1yfwvtH_gGnQpG7</recordid><startdate>20070801</startdate><enddate>20070801</enddate><creator>Zeng, Xianzhong</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>20070801</creationdate><title>Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains</title><author>Zeng, Xianzhong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-dc6b9f4e284eea39350f764a7c04dc63ecb069a908bde0769a78781c43aad7ca3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Blow-up</topic><topic>Critical exponent</topic><topic>Exact sciences and technology</topic><topic>Exterior domain</topic><topic>Global analysis, analysis on manifolds</topic><topic>Global existence</topic><topic>Inhomogeneous boundary conditions</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>The evolution P-Laplacian equations</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zeng, Xianzhong</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>Zeng, Xianzhong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains</atitle><jtitle>Nonlinear analysis</jtitle><date>2007-08-01</date><risdate>2007</risdate><volume>67</volume><issue>3</issue><spage>901</spage><epage>916</epage><pages>901-916</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that
q
c
=
n
(
p
−
1
)
/
(
n
−
p
)
is its critical exponent provided
2
n
/
(
n
+
1
)
<
p
<
n
. Furthermore, we prove that if
max
{
1
,
p
−
1
}
<
q
≤
q
c
, then every positive solution of the equations blows up in finite time; whereas for
q
>
q
c
, the equations admit the global positive solutions for some boundary value
f
(
x
)
and some initial data
u
0
(
x
)
. We also demonstrate that every positive solution of the equations blows up in finite time provided
n
≤
p
.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2006.06.048</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2007-08, Vol.67 (3), p.901-916 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_29984410 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Blow-up Critical exponent Exact sciences and technology Exterior domain Global analysis, analysis on manifolds Global existence Inhomogeneous boundary conditions Mathematical analysis Mathematics Partial differential equations Sciences and techniques of general use The evolution P-Laplacian equations Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T19%3A48%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Existence%20and%20nonexistence%20of%20global%20positive%20solutions%20for%20the%20evolution%20P-Laplacian%20equations%20in%20exterior%20domains&rft.jtitle=Nonlinear%20analysis&rft.au=Zeng,%20Xianzhong&rft.date=2007-08-01&rft.volume=67&rft.issue=3&rft.spage=901&rft.epage=916&rft.pages=901-916&rft.issn=0362-546X&rft.eissn=1873-5215&rft.coden=NOANDD&rft_id=info:doi/10.1016/j.na.2006.06.048&rft_dat=%3Cproquest_cross%3E29984410%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=29984410&rft_id=info:pmid/&rft_els_id=S0362546X06003646&rfr_iscdi=true |