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Prescribed Mass Solutions to Schrödinger Systems With linear Coupled Terms
We consider the existence of normalized solutions to the following nonlinear Schrödinger system - Δ u + λ 1 u = μ 1 | u | p - 2 u + β v in R N , - Δ v + λ 2 v = μ 2 | v | q - 2 v + β u in R N , under the mass constraints ∫ R N | u | 2 d x = a 1 2 and ∫ R N | v | 2 d x = a 2 2 , where 2 < p ≤ 2 +...
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| Published in: | The Journal of geometric analysis 2023-11, Vol.33 (11), Article 347 |
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| Language: | English |
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| container_title | The Journal of geometric analysis |
| container_volume | 33 |
| creator | Chen, Haixia Yang, Xiaolong |
| description | We consider the existence of normalized solutions to the following nonlinear Schrödinger system
-
Δ
u
+
λ
1
u
=
μ
1
|
u
|
p
-
2
u
+
β
v
in
R
N
,
-
Δ
v
+
λ
2
v
=
μ
2
|
v
|
q
-
2
v
+
β
u
in
R
N
,
under the mass constraints
∫
R
N
|
u
|
2
d
x
=
a
1
2
and
∫
R
N
|
v
|
2
d
x
=
a
2
2
,
where
2
<
p
≤
2
+
4
N
≤
q
≤
2
∗
,
β
,
μ
1
,
μ
2
>
0
,
a
1
,
a
2
>
0
, and
λ
1
,
λ
2
∈
R
appear as Lagrange multipliers. Under different character on
p
,
q
with respect to the mass critical exponent, we prove several existence results and precise asymptotic behavior of these solutions as
(
a
1
,
a
2
)
→
(
0
,
0
)
. These cases present substantial differences with respect to purely mass subcritical or mass supercritical situations. |
| doi_str_mv | 10.1007/s12220-023-01405-8 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2852693678</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2852693678</sourcerecordid><originalsourceid>FETCH-LOGICAL-c309t-a3d8ca130e5a6d61396297f73efbfcc48cb832e0584eac59d928b1414a7e71f33</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EElD4AVaWWBvGz9hLVPESRSC1CHaW4zg0VZoUO1n0x_gBfoyUILFjNbO4547mIHRG4YICZJeJMsaAAOMEqABJ9B46olIaAsDe9ocdJBBlmDpExymtAITiIjtCD88xJB-rPBT40aWE523dd1XbJNy1eO6X8euzqJr3EPF8m7qwTvi16pa4rprgIp62_aYe0EWI63SCDkpXp3D6Oyfo5eZ6Mb0js6fb--nVjHgOpiOOF9o7yiFIpwpFuVHMZGXGQ5mX3gvtc81ZAKlFcF6awjCdU0GFy0JGS84n6Hzs3cT2ow-ps6u2j81w0jItmTJcZXpIsTHlY5tSDKXdxGrt4tZSsDtpdpRmB2n2R5rdQXyE0hDeff1X_Q_1DX8Kb_U</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2852693678</pqid></control><display><type>article</type><title>Prescribed Mass Solutions to Schrödinger Systems With linear Coupled Terms</title><source>Springer Nature</source><creator>Chen, Haixia ; Yang, Xiaolong</creator><creatorcontrib>Chen, Haixia ; Yang, Xiaolong</creatorcontrib><description>We consider the existence of normalized solutions to the following nonlinear Schrödinger system
-
Δ
u
+
λ
1
u
=
μ
1
|
u
|
p
-
2
u
+
β
v
in
R
N
,
-
Δ
v
+
λ
2
v
=
μ
2
|
v
|
q
-
2
v
+
β
u
in
R
N
,
under the mass constraints
∫
R
N
|
u
|
2
d
x
=
a
1
2
and
∫
R
N
|
v
|
2
d
x
=
a
2
2
,
where
2
<
p
≤
2
+
4
N
≤
q
≤
2
∗
,
β
,
μ
1
,
μ
2
>
0
,
a
1
,
a
2
>
0
, and
λ
1
,
λ
2
∈
R
appear as Lagrange multipliers. Under different character on
p
,
q
with respect to the mass critical exponent, we prove several existence results and precise asymptotic behavior of these solutions as
(
a
1
,
a
2
)
→
(
0
,
0
)
. These cases present substantial differences with respect to purely mass subcritical or mass supercritical situations.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-023-01405-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Asymptotic properties ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Lagrange multiplier ; Mathematics ; Mathematics and Statistics</subject><ispartof>The Journal of geometric analysis, 2023-11, Vol.33 (11), Article 347</ispartof><rights>Mathematica Josephina, Inc. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c309t-a3d8ca130e5a6d61396297f73efbfcc48cb832e0584eac59d928b1414a7e71f33</cites><orcidid>0000-0002-7648-254X</orcidid></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>Chen, Haixia</creatorcontrib><creatorcontrib>Yang, Xiaolong</creatorcontrib><title>Prescribed Mass Solutions to Schrödinger Systems With linear Coupled Terms</title><title>The Journal of geometric analysis</title><addtitle>J Geom Anal</addtitle><description>We consider the existence of normalized solutions to the following nonlinear Schrödinger system
-
Δ
u
+
λ
1
u
=
μ
1
|
u
|
p
-
2
u
+
β
v
in
R
N
,
-
Δ
v
+
λ
2
v
=
μ
2
|
v
|
q
-
2
v
+
β
u
in
R
N
,
under the mass constraints
∫
R
N
|
u
|
2
d
x
=
a
1
2
and
∫
R
N
|
v
|
2
d
x
=
a
2
2
,
where
2
<
p
≤
2
+
4
N
≤
q
≤
2
∗
,
β
,
μ
1
,
μ
2
>
0
,
a
1
,
a
2
>
0
, and
λ
1
,
λ
2
∈
R
appear as Lagrange multipliers. Under different character on
p
,
q
with respect to the mass critical exponent, we prove several existence results and precise asymptotic behavior of these solutions as
(
a
1
,
a
2
)
→
(
0
,
0
)
. These cases present substantial differences with respect to purely mass subcritical or mass supercritical situations.</description><subject>Abstract Harmonic Analysis</subject><subject>Asymptotic properties</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Lagrange multiplier</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EElD4AVaWWBvGz9hLVPESRSC1CHaW4zg0VZoUO1n0x_gBfoyUILFjNbO4547mIHRG4YICZJeJMsaAAOMEqABJ9B46olIaAsDe9ocdJBBlmDpExymtAITiIjtCD88xJB-rPBT40aWE523dd1XbJNy1eO6X8euzqJr3EPF8m7qwTvi16pa4rprgIp62_aYe0EWI63SCDkpXp3D6Oyfo5eZ6Mb0js6fb--nVjHgOpiOOF9o7yiFIpwpFuVHMZGXGQ5mX3gvtc81ZAKlFcF6awjCdU0GFy0JGS84n6Hzs3cT2ow-ps6u2j81w0jItmTJcZXpIsTHlY5tSDKXdxGrt4tZSsDtpdpRmB2n2R5rdQXyE0hDeff1X_Q_1DX8Kb_U</recordid><startdate>20231101</startdate><enddate>20231101</enddate><creator>Chen, Haixia</creator><creator>Yang, Xiaolong</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-7648-254X</orcidid></search><sort><creationdate>20231101</creationdate><title>Prescribed Mass Solutions to Schrödinger Systems With linear Coupled Terms</title><author>Chen, Haixia ; Yang, Xiaolong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c309t-a3d8ca130e5a6d61396297f73efbfcc48cb832e0584eac59d928b1414a7e71f33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Asymptotic properties</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Lagrange multiplier</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Haixia</creatorcontrib><creatorcontrib>Yang, Xiaolong</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of geometric analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Haixia</au><au>Yang, Xiaolong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Prescribed Mass Solutions to Schrödinger Systems With linear Coupled Terms</atitle><jtitle>The Journal of geometric analysis</jtitle><stitle>J Geom Anal</stitle><date>2023-11-01</date><risdate>2023</risdate><volume>33</volume><issue>11</issue><artnum>347</artnum><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>We consider the existence of normalized solutions to the following nonlinear Schrödinger system
-
Δ
u
+
λ
1
u
=
μ
1
|
u
|
p
-
2
u
+
β
v
in
R
N
,
-
Δ
v
+
λ
2
v
=
μ
2
|
v
|
q
-
2
v
+
β
u
in
R
N
,
under the mass constraints
∫
R
N
|
u
|
2
d
x
=
a
1
2
and
∫
R
N
|
v
|
2
d
x
=
a
2
2
,
where
2
<
p
≤
2
+
4
N
≤
q
≤
2
∗
,
β
,
μ
1
,
μ
2
>
0
,
a
1
,
a
2
>
0
, and
λ
1
,
λ
2
∈
R
appear as Lagrange multipliers. Under different character on
p
,
q
with respect to the mass critical exponent, we prove several existence results and precise asymptotic behavior of these solutions as
(
a
1
,
a
2
)
→
(
0
,
0
)
. These cases present substantial differences with respect to purely mass subcritical or mass supercritical situations.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-023-01405-8</doi><orcidid>https://orcid.org/0000-0002-7648-254X</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1050-6926 |
| ispartof | The Journal of geometric analysis, 2023-11, Vol.33 (11), Article 347 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_proquest_journals_2852693678 |
| source | Springer Nature |
| subjects | Abstract Harmonic Analysis Asymptotic properties Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Lagrange multiplier Mathematics Mathematics and Statistics |
| title | Prescribed Mass Solutions to Schrödinger Systems With linear Coupled Terms |
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