Positive solutions of elliptic equations with nonlinear boundary conditions
This paper deals with the nonlinear elliptic equation − Δ u + u = f ( x , u ) in a bounded smooth domain Ω ⊂ R N with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.
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| Veröffentlicht in: | Nonlinear analysis 2009, Vol.70 (1), p.328-334 |
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| container_end_page | 334 |
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| container_title | Nonlinear analysis |
| container_volume | 70 |
| creator | Song, Xiuchao Wang, Weihua Zhao, Peihao |
| description | This paper deals with the nonlinear elliptic equation
−
Δ
u
+
u
=
f
(
x
,
u
)
in a bounded smooth domain
Ω
⊂
R
N
with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered. |
| doi_str_mv | 10.1016/j.na.2007.12.003 |
| format | Article |
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−
Δ
u
+
u
=
f
(
x
,
u
)
in a bounded smooth domain
Ω
⊂
R
N
with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2007.12.003</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Coercive ; Exact sciences and technology ; Mathematical analysis ; Mathematics ; Mountain Pass Lemma ; Nonlinear boundary value condition ; Nonlinear elliptic equation ; Partial differential equations ; Sciences and techniques of general use ; Sub–supersolution ; Weakly lower semi-continuous</subject><ispartof>Nonlinear analysis, 2009, Vol.70 (1), p.328-334</ispartof><rights>2007 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-e73d3b7c6991d930f709ef544320e8e854c3c1d3dee9a981dca36adfe45d68563</citedby><cites>FETCH-LOGICAL-c355t-e73d3b7c6991d930f709ef544320e8e854c3c1d3dee9a981dca36adfe45d68563</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.2007.12.003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,4024,27923,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20919176$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Song, Xiuchao</creatorcontrib><creatorcontrib>Wang, Weihua</creatorcontrib><creatorcontrib>Zhao, Peihao</creatorcontrib><title>Positive solutions of elliptic equations with nonlinear boundary conditions</title><title>Nonlinear analysis</title><description>This paper deals with the nonlinear elliptic equation
−
Δ
u
+
u
=
f
(
x
,
u
)
in a bounded smooth domain
Ω
⊂
R
N
with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.</description><subject>Coercive</subject><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mountain Pass Lemma</subject><subject>Nonlinear boundary value condition</subject><subject>Nonlinear elliptic equation</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Sub–supersolution</subject><subject>Weakly lower semi-continuous</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp1UM1LwzAUD6LgnN499qK31pemSRtvMvzCgR4UvIUsecWMLtmSVvG_t3PDm6cHj983IecUCgpUXC0Lr4sSoC5oWQCwAzKhTc1yXlJ-SCbARJnzSrwfk5OUlgBAayYm5OklJNe7T8xS6IbeBZ-y0GbYdW7dO5PhZtC775frPzIffOc86pgtwuCtjt-ZCd66X8gpOWp1l_Bsf6fk7e72dfaQz5_vH2c389wwzvsca2bZojZCSmolg7YGiS2vKlYCNtjwyjBDLbOIUsuGWqOZ0LbFilvRcMGm5HKnu45hM2Dq1colM0bWHsOQ1OgiGjaWnxLYAU0MKUVs1Tq61RhaUVDb1dRSea22qylaqnG1kXKx19bJ6K6N2huX_nglSCppvc1wvcPhWPTTYVTJOPQGrYtoemWD-9_kB8kdgrY</recordid><startdate>2009</startdate><enddate>2009</enddate><creator>Song, Xiuchao</creator><creator>Wang, Weihua</creator><creator>Zhao, Peihao</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>2009</creationdate><title>Positive solutions of elliptic equations with nonlinear boundary conditions</title><author>Song, Xiuchao ; Wang, Weihua ; Zhao, Peihao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-e73d3b7c6991d930f709ef544320e8e854c3c1d3dee9a981dca36adfe45d68563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Coercive</topic><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mountain Pass Lemma</topic><topic>Nonlinear boundary value condition</topic><topic>Nonlinear elliptic equation</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Sub–supersolution</topic><topic>Weakly lower semi-continuous</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Song, Xiuchao</creatorcontrib><creatorcontrib>Wang, Weihua</creatorcontrib><creatorcontrib>Zhao, Peihao</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>Song, Xiuchao</au><au>Wang, Weihua</au><au>Zhao, Peihao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Positive solutions of elliptic equations with nonlinear boundary conditions</atitle><jtitle>Nonlinear analysis</jtitle><date>2009</date><risdate>2009</risdate><volume>70</volume><issue>1</issue><spage>328</spage><epage>334</epage><pages>328-334</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>This paper deals with the nonlinear elliptic equation
−
Δ
u
+
u
=
f
(
x
,
u
)
in a bounded smooth domain
Ω
⊂
R
N
with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2007.12.003</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2009, Vol.70 (1), p.328-334 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_35568387 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | Coercive Exact sciences and technology Mathematical analysis Mathematics Mountain Pass Lemma Nonlinear boundary value condition Nonlinear elliptic equation Partial differential equations Sciences and techniques of general use Sub–supersolution Weakly lower semi-continuous |
| title | Positive solutions of elliptic equations with nonlinear boundary conditions |
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