Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems
In this paper, we are concerned with the existence and concentration of ground state solutions for the following nonlinear Schrödinger–Poisson-type system with doubly critical growth - ε 2 Δ u + V ( x ) u - ϕ | u | 3 u = | u | 4 u + f ( u ) , in R 3 , - ε 2 Δ ϕ = | u | 5 , in R 3 , where ε > 0 is...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2020-10, Vol.71 (5), Article 154 |
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| creator | Feng, Xiaojing |
| description | In this paper, we are concerned with the existence and concentration of ground state solutions for the following nonlinear Schrödinger–Poisson-type system with doubly critical growth
-
ε
2
Δ
u
+
V
(
x
)
u
-
ϕ
|
u
|
3
u
=
|
u
|
4
u
+
f
(
u
)
,
in
R
3
,
-
ε
2
Δ
ϕ
=
|
u
|
5
,
in
R
3
,
where
ε
>
0
is a small parameter. By employing the concentration-compactness principle and mountain pass theorem, we prove the existence of positive ground state solutions
v
ε
with exponential decay at infinity for
ε
sufficiently small under some suitable assumptions on the potential
V
and nonlinearity
f
. Moreover, as
ε
→
0
+
,
v
ε
concentrates around a global minimum point of
V
. |
| doi_str_mv | 10.1007/s00033-020-01381-x |
| format | Article |
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-
ε
2
Δ
u
+
V
(
x
)
u
-
ϕ
|
u
|
3
u
=
|
u
|
4
u
+
f
(
u
)
,
in
R
3
,
-
ε
2
Δ
ϕ
=
|
u
|
5
,
in
R
3
,
where
ε
>
0
is a small parameter. By employing the concentration-compactness principle and mountain pass theorem, we prove the existence of positive ground state solutions
v
ε
with exponential decay at infinity for
ε
sufficiently small under some suitable assumptions on the potential
V
and nonlinearity
f
. Moreover, as
ε
→
0
+
,
v
ε
concentrates around a global minimum point of
V
.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-020-01381-x</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Engineering ; Existence theorems ; Ground state ; Mathematical Methods in Physics ; Mountains ; Nonlinearity ; Theoretical and Applied Mechanics</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2020-10, Vol.71 (5), Article 154</ispartof><rights>Springer Nature Switzerland AG 2020</rights><rights>Springer Nature Switzerland AG 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-d199823189dea0b472bf97b919276c2c0b6ed07e34ecf761d83fa49d25631d5f3</citedby><cites>FETCH-LOGICAL-c319t-d199823189dea0b472bf97b919276c2c0b6ed07e34ecf761d83fa49d25631d5f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00033-020-01381-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-020-01381-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Feng, Xiaojing</creatorcontrib><title>Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>In this paper, we are concerned with the existence and concentration of ground state solutions for the following nonlinear Schrödinger–Poisson-type system with doubly critical growth
-
ε
2
Δ
u
+
V
(
x
)
u
-
ϕ
|
u
|
3
u
=
|
u
|
4
u
+
f
(
u
)
,
in
R
3
,
-
ε
2
Δ
ϕ
=
|
u
|
5
,
in
R
3
,
where
ε
>
0
is a small parameter. By employing the concentration-compactness principle and mountain pass theorem, we prove the existence of positive ground state solutions
v
ε
with exponential decay at infinity for
ε
sufficiently small under some suitable assumptions on the potential
V
and nonlinearity
f
. Moreover, as
ε
→
0
+
,
v
ε
concentrates around a global minimum point of
V
.</description><subject>Engineering</subject><subject>Existence theorems</subject><subject>Ground state</subject><subject>Mathematical Methods in Physics</subject><subject>Mountains</subject><subject>Nonlinearity</subject><subject>Theoretical and Applied Mechanics</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9UEtKxDAYDqLgOHoBVwHX1T9J2zRLGXzBgIK6DmmSjh06zZikMLPzDt7FC3gTT2LGCu5c_a_vwf8hdErgnADwiwAAjGVAIQPCKpJt9tCE5GkUwMQ-mgDkeUYpLw7RUQjLBOcE2AStrjZtiLbXFqveYO1S10evYut67Bq88G5I-xBVtDi4btgdAm6cx8YNdbfF2rex1arDj_rFf36Ytl9Y__X2_uDaEFyfxe06MbfJZBWO0UGjumBPfusUPV9fPc1us_n9zd3scp5pRkTMDBGiooxUwlgFdc5p3QheCyIoLzXVUJfWALcst7rhJTEVa1QuDC1KRkzRsCk6G3XX3r0ONkS5dIPvk6WkOeNVxaqCJhQdUdq7ELxt5Nq3K-W3koDcxSrHWGWKVf7EKjeJxEZSSODdq3_S_7C-AXPtfyc</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>Feng, Xiaojing</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201001</creationdate><title>Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems</title><author>Feng, Xiaojing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-d199823189dea0b472bf97b919276c2c0b6ed07e34ecf761d83fa49d25631d5f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Engineering</topic><topic>Existence theorems</topic><topic>Ground state</topic><topic>Mathematical Methods in Physics</topic><topic>Mountains</topic><topic>Nonlinearity</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Feng, Xiaojing</creatorcontrib><collection>CrossRef</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Feng, Xiaojing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2020-10-01</date><risdate>2020</risdate><volume>71</volume><issue>5</issue><artnum>154</artnum><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>In this paper, we are concerned with the existence and concentration of ground state solutions for the following nonlinear Schrödinger–Poisson-type system with doubly critical growth
-
ε
2
Δ
u
+
V
(
x
)
u
-
ϕ
|
u
|
3
u
=
|
u
|
4
u
+
f
(
u
)
,
in
R
3
,
-
ε
2
Δ
ϕ
=
|
u
|
5
,
in
R
3
,
where
ε
>
0
is a small parameter. By employing the concentration-compactness principle and mountain pass theorem, we prove the existence of positive ground state solutions
v
ε
with exponential decay at infinity for
ε
sufficiently small under some suitable assumptions on the potential
V
and nonlinearity
f
. Moreover, as
ε
→
0
+
,
v
ε
concentrates around a global minimum point of
V
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-020-01381-x</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0044-2275 |
| ispartof | Zeitschrift für angewandte Mathematik und Physik, 2020-10, Vol.71 (5), Article 154 |
| issn | 0044-2275 1420-9039 |
| language | eng |
| recordid | cdi_proquest_journals_2437883852 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Engineering Existence theorems Ground state Mathematical Methods in Physics Mountains Nonlinearity Theoretical and Applied Mechanics |
| title | Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems |
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