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Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities
We study the behavior near the origin of C 2 positive solutions u ( x ) and v ( x ) of the system 0 ≤ - Δ u ≤ 1 | x | α ∗ v λ 0 ≤ - Δ v ≤ 1 | x | β ∗ u σ in B 2 ( 0 ) \ { 0 } ⊂ R n , n ≥ 3 , where λ , σ ≥ 0 and α , β ∈ ( 0 , n ) . A by-product of our methods used to study these solutions will be res...
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| Published in: | Calculus of variations and partial differential equations 2015-10, Vol.54 (2), p.1243-1273 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c358t-423df4e1ad498c8c5123abaaaf3c7f60ae7675a3d0f209f7488046e23e1261913 |
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| cites | cdi_FETCH-LOGICAL-c358t-423df4e1ad498c8c5123abaaaf3c7f60ae7675a3d0f209f7488046e23e1261913 |
| container_end_page | 1273 |
| container_issue | 2 |
| container_start_page | 1243 |
| container_title | Calculus of variations and partial differential equations |
| container_volume | 54 |
| creator | Ghergu, Marius Taliaferro, Steven D. |
| description | We study the behavior near the origin of
C
2
positive solutions
u
(
x
)
and
v
(
x
)
of the system
0
≤
-
Δ
u
≤
1
|
x
|
α
∗
v
λ
0
≤
-
Δ
v
≤
1
|
x
|
β
∗
u
σ
in
B
2
(
0
)
\
{
0
}
⊂
R
n
,
n
≥
3
,
where
λ
,
σ
≥
0
and
α
,
β
∈
(
0
,
n
)
. A by-product of our methods used to study these solutions will be results on the behavior near the origin of
L
1
(
B
1
(
0
)
)
solutions
f
and
g
of the system
0
≤
f
(
x
)
≤
C
|
x
|
2
-
α
+
∫
|
y
|
<
1
g
(
y
)
d
y
|
x
-
y
|
α
-
2
λ
0
≤
g
(
x
)
≤
C
|
x
|
2
-
β
+
∫
|
y
|
<
1
f
(
y
)
d
y
|
x
-
y
|
β
-
2
σ
for
0
<
|
x
|
<
1
where
λ
,
σ
≥
0
and
α
,
β
∈
(
2
,
n
+
2
)
. |
| doi_str_mv | 10.1007/s00526-015-0824-3 |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s00526_015_0824_3</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s00526_015_0824_3</sourcerecordid><originalsourceid>FETCH-LOGICAL-c358t-423df4e1ad498c8c5123abaaaf3c7f60ae7675a3d0f209f7488046e23e1261913</originalsourceid><addsrcrecordid>eNp9kMtKAzEUhoMoWKsP4C4vMJrb3JaleIOCG12H05mkpmQmNScj9O1NO65dhcP__T_hI-SeswfOWP2IjJWiKhgvC9YIVcgLsuBKinzJ8pIsWKtUIaqqvSY3iHuWwYwtCK7wOBxSSK6jW_MFPy5ECok6DB6S6Sm6cTd5iC45g9TmNCdTcmFEGiwdw-hDB56iGZx3o4FIjffucBrEIyYznLmcfE_gzyu35MqCR3P39y7J5_PTx_q12Ly_vK1Xm6KTZZMKJWRvleHQq7bpmq7kQsIWAKzsalsxMHVVlyB7ZgVrba2ahqnKCGm4qHjL5ZLwebeLATEaqw_RDRCPmjN9sqZnazrL0CdrWuaOmDuY2XFnot6HKY75m_-UfgHwcXMl</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities</title><source>Springer Nature</source><creator>Ghergu, Marius ; Taliaferro, Steven D.</creator><creatorcontrib>Ghergu, Marius ; Taliaferro, Steven D.</creatorcontrib><description>We study the behavior near the origin of
C
2
positive solutions
u
(
x
)
and
v
(
x
)
of the system
0
≤
-
Δ
u
≤
1
|
x
|
α
∗
v
λ
0
≤
-
Δ
v
≤
1
|
x
|
β
∗
u
σ
in
B
2
(
0
)
\
{
0
}
⊂
R
n
,
n
≥
3
,
where
λ
,
σ
≥
0
and
α
,
β
∈
(
0
,
n
)
. A by-product of our methods used to study these solutions will be results on the behavior near the origin of
L
1
(
B
1
(
0
)
)
solutions
f
and
g
of the system
0
≤
f
(
x
)
≤
C
|
x
|
2
-
α
+
∫
|
y
|
<
1
g
(
y
)
d
y
|
x
-
y
|
α
-
2
λ
0
≤
g
(
x
)
≤
C
|
x
|
2
-
β
+
∫
|
y
|
<
1
f
(
y
)
d
y
|
x
-
y
|
β
-
2
σ
for
0
<
|
x
|
<
1
where
λ
,
σ
≥
0
and
α
,
β
∈
(
2
,
n
+
2
)
.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-015-0824-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of Variations and Optimal Control; Optimization ; Control ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Systems Theory ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2015-10, Vol.54 (2), p.1243-1273</ispartof><rights>Springer-Verlag Berlin Heidelberg 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-423df4e1ad498c8c5123abaaaf3c7f60ae7675a3d0f209f7488046e23e1261913</citedby><cites>FETCH-LOGICAL-c358t-423df4e1ad498c8c5123abaaaf3c7f60ae7675a3d0f209f7488046e23e1261913</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Ghergu, Marius</creatorcontrib><creatorcontrib>Taliaferro, Steven D.</creatorcontrib><title>Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>We study the behavior near the origin of
C
2
positive solutions
u
(
x
)
and
v
(
x
)
of the system
0
≤
-
Δ
u
≤
1
|
x
|
α
∗
v
λ
0
≤
-
Δ
v
≤
1
|
x
|
β
∗
u
σ
in
B
2
(
0
)
\
{
0
}
⊂
R
n
,
n
≥
3
,
where
λ
,
σ
≥
0
and
α
,
β
∈
(
0
,
n
)
. A by-product of our methods used to study these solutions will be results on the behavior near the origin of
L
1
(
B
1
(
0
)
)
solutions
f
and
g
of the system
0
≤
f
(
x
)
≤
C
|
x
|
2
-
α
+
∫
|
y
|
<
1
g
(
y
)
d
y
|
x
-
y
|
α
-
2
λ
0
≤
g
(
x
)
≤
C
|
x
|
2
-
β
+
∫
|
y
|
<
1
f
(
y
)
d
y
|
x
-
y
|
β
-
2
σ
for
0
<
|
x
|
<
1
where
λ
,
σ
≥
0
and
α
,
β
∈
(
2
,
n
+
2
)
.</description><subject>Analysis</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsP4C4vMJrb3JaleIOCG12H05mkpmQmNScj9O1NO65dhcP__T_hI-SeswfOWP2IjJWiKhgvC9YIVcgLsuBKinzJ8pIsWKtUIaqqvSY3iHuWwYwtCK7wOBxSSK6jW_MFPy5ECok6DB6S6Sm6cTd5iC45g9TmNCdTcmFEGiwdw-hDB56iGZx3o4FIjffucBrEIyYznLmcfE_gzyu35MqCR3P39y7J5_PTx_q12Ly_vK1Xm6KTZZMKJWRvleHQq7bpmq7kQsIWAKzsalsxMHVVlyB7ZgVrba2ahqnKCGm4qHjL5ZLwebeLATEaqw_RDRCPmjN9sqZnazrL0CdrWuaOmDuY2XFnot6HKY75m_-UfgHwcXMl</recordid><startdate>20151001</startdate><enddate>20151001</enddate><creator>Ghergu, Marius</creator><creator>Taliaferro, Steven D.</creator><general>Springer Berlin Heidelberg</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20151001</creationdate><title>Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities</title><author>Ghergu, Marius ; Taliaferro, Steven D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-423df4e1ad498c8c5123abaaaf3c7f60ae7675a3d0f209f7488046e23e1261913</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ghergu, Marius</creatorcontrib><creatorcontrib>Taliaferro, Steven D.</creatorcontrib><collection>CrossRef</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ghergu, Marius</au><au>Taliaferro, Steven D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2015-10-01</date><risdate>2015</risdate><volume>54</volume><issue>2</issue><spage>1243</spage><epage>1273</epage><pages>1243-1273</pages><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We study the behavior near the origin of
C
2
positive solutions
u
(
x
)
and
v
(
x
)
of the system
0
≤
-
Δ
u
≤
1
|
x
|
α
∗
v
λ
0
≤
-
Δ
v
≤
1
|
x
|
β
∗
u
σ
in
B
2
(
0
)
\
{
0
}
⊂
R
n
,
n
≥
3
,
where
λ
,
σ
≥
0
and
α
,
β
∈
(
0
,
n
)
. A by-product of our methods used to study these solutions will be results on the behavior near the origin of
L
1
(
B
1
(
0
)
)
solutions
f
and
g
of the system
0
≤
f
(
x
)
≤
C
|
x
|
2
-
α
+
∫
|
y
|
<
1
g
(
y
)
d
y
|
x
-
y
|
α
-
2
λ
0
≤
g
(
x
)
≤
C
|
x
|
2
-
β
+
∫
|
y
|
<
1
f
(
y
)
d
y
|
x
-
y
|
β
-
2
σ
for
0
<
|
x
|
<
1
where
λ
,
σ
≥
0
and
α
,
β
∈
(
2
,
n
+
2
)
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-015-0824-3</doi><tpages>31</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0944-2669 |
| ispartof | Calculus of variations and partial differential equations, 2015-10, Vol.54 (2), p.1243-1273 |
| issn | 0944-2669 1432-0835 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s00526_015_0824_3 |
| source | Springer Nature |
| subjects | Analysis Calculus of Variations and Optimal Control Optimization Control Mathematical and Computational Physics Mathematics Mathematics and Statistics Systems Theory Theoretical |
| title | Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities |
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