Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains
The goal of this paper is to study the existence of non-trivial weak solutions for the nonuniformly nonlinear elliptic equation − div ( h ( x ) ∇ u ) + q ( x ) u = f ( x , u ) in an unbounded domain Ω ⊂ R N ( N ≥ 3 ) , where h ( x ) ∈ L loc 1 ( Ω ) . The solutions will be obtained in a subspace of t...
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| Veröffentlicht in: | Nonlinear analysis 2009-06, Vol.70 (11), p.3987-3996 |
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| creator | Toan, Hoang Quoc Chung, Nguyen Thanh |
| description | The goal of this paper is to study the existence of non-trivial weak solutions for the nonuniformly nonlinear elliptic equation
−
div
(
h
(
x
)
∇
u
)
+
q
(
x
)
u
=
f
(
x
,
u
)
in an unbounded domain
Ω
⊂
R
N
(
N
≥
3
)
, where
h
(
x
)
∈
L
loc
1
(
Ω
)
. The solutions will be obtained in a subspace of the Sobolev space
H
0
1
(
Ω
)
and the proofs rely essentially on a variation of the Mountain pass theorem in [D.M. Duc, Nonlinear singular elliptic equations, J. London. Math. Soc. 40 (2) (1989) 420–440]. |
| doi_str_mv | 10.1016/j.na.2008.08.007 |
| format | Article |
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−
div
(
h
(
x
)
∇
u
)
+
q
(
x
)
u
=
f
(
x
,
u
)
in an unbounded domain
Ω
⊂
R
N
(
N
≥
3
)
, where
h
(
x
)
∈
L
loc
1
(
Ω
)
. The solutions will be obtained in a subspace of the Sobolev space
H
0
1
(
Ω
)
and the proofs rely essentially on a variation of the Mountain pass theorem in [D.M. Duc, Nonlinear singular elliptic equations, J. London. Math. Soc. 40 (2) (1989) 420–440].</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2008.08.007</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Exact sciences and technology ; Mathematical analysis ; Mathematics ; Mountain pass theorem ; Nonuniformly elliptic equations ; Partial differential equations ; Sciences and techniques of general use ; The weakly continuously differentiable functional</subject><ispartof>Nonlinear analysis, 2009-06, Vol.70 (11), p.3987-3996</ispartof><rights>2008 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-2f310fdd418677d534929285d33b57f4f6d1424616e7fa82947c17e787f63a5c3</citedby><cites>FETCH-LOGICAL-c355t-2f310fdd418677d534929285d33b57f4f6d1424616e7fa82947c17e787f63a5c3</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.2008.08.007$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21343494$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Toan, Hoang Quoc</creatorcontrib><creatorcontrib>Chung, Nguyen Thanh</creatorcontrib><title>Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains</title><title>Nonlinear analysis</title><description>The goal of this paper is to study the existence of non-trivial weak solutions for the nonuniformly nonlinear elliptic equation
−
div
(
h
(
x
)
∇
u
)
+
q
(
x
)
u
=
f
(
x
,
u
)
in an unbounded domain
Ω
⊂
R
N
(
N
≥
3
)
, where
h
(
x
)
∈
L
loc
1
(
Ω
)
. The solutions will be obtained in a subspace of the Sobolev space
H
0
1
(
Ω
)
and the proofs rely essentially on a variation of the Mountain pass theorem in [D.M. Duc, Nonlinear singular elliptic equations, J. London. Math. Soc. 40 (2) (1989) 420–440].</description><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mountain pass theorem</subject><subject>Nonuniformly elliptic equations</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>The weakly continuously differentiable functional</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp1UMlKBDEQDaLguNw95qK3HrOnx5uIGwheFLyFmAUy9iQzqW51_t5uRrwJBUVVvfeq6iF0RsmcEqoul_Ns54yQdj4F0XtoRlvNG8mo3EczwhVrpFBvh-gIYEkIoZqrGUq33wn6kF3AJeKvYD8wlG7oU8mAY6nYYtdZgGmaSx5yGpurbjsVXcrBVhy6Lq375HDYDHZHTBkP-b0M2QePfVnZlOEEHUTbQTj9zcfo9e725eaheXq-f7y5fmocl7JvWOSURO8FbZXWXnKxYAvWSs_5u9RRROWpYEJRFXS0LVsI7agOutVRcSsdP0YXO911LZshQG9WCdx4pM2hDGC4kILJhR6BZAd0tQDUEM26ppWtW0OJmTw1S5OtmTw1U5CJcv6rbcHZLlabXYI_HqNcjPeKEXe1w4Xx0c8UqgGXJpN9qsH1xpf0_5Ifl5qMRw</recordid><startdate>20090601</startdate><enddate>20090601</enddate><creator>Toan, Hoang Quoc</creator><creator>Chung, Nguyen Thanh</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>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20090601</creationdate><title>Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains</title><author>Toan, Hoang Quoc ; Chung, Nguyen Thanh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-2f310fdd418677d534929285d33b57f4f6d1424616e7fa82947c17e787f63a5c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mountain pass theorem</topic><topic>Nonuniformly elliptic equations</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>The weakly continuously differentiable functional</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Toan, Hoang Quoc</creatorcontrib><creatorcontrib>Chung, Nguyen Thanh</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>Aerospace 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>Toan, Hoang Quoc</au><au>Chung, Nguyen Thanh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains</atitle><jtitle>Nonlinear analysis</jtitle><date>2009-06-01</date><risdate>2009</risdate><volume>70</volume><issue>11</issue><spage>3987</spage><epage>3996</epage><pages>3987-3996</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>The goal of this paper is to study the existence of non-trivial weak solutions for the nonuniformly nonlinear elliptic equation
−
div
(
h
(
x
)
∇
u
)
+
q
(
x
)
u
=
f
(
x
,
u
)
in an unbounded domain
Ω
⊂
R
N
(
N
≥
3
)
, where
h
(
x
)
∈
L
loc
1
(
Ω
)
. The solutions will be obtained in a subspace of the Sobolev space
H
0
1
(
Ω
)
and the proofs rely essentially on a variation of the Mountain pass theorem in [D.M. Duc, Nonlinear singular elliptic equations, J. London. Math. Soc. 40 (2) (1989) 420–440].</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2008.08.007</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2009-06, Vol.70 (11), p.3987-3996 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_34542597 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Exact sciences and technology Mathematical analysis Mathematics Mountain pass theorem Nonuniformly elliptic equations Partial differential equations Sciences and techniques of general use The weakly continuously differentiable functional |
| title | Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains |
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