Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations
In this paper, we study the following equations 0.1 i ϕ t = - A ( | | ∇ ϕ | | 2 ) Δ ϕ - | ϕ | p - 1 ϕ , t > 0 , x ∈ R n , ϕ ( x , 0 ) = ϕ 0 ( x ) ∈ H 1 ( R n ) , where n ≥ 1 , 1 < p < n + 4 n , A ( s ) is a function. Under suitable conditions on A ( s ), we use Lyapunov method to prove the...
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| Veröffentlicht in: | Mediterranean journal of mathematics 2022-02, Vol.19 (1), Article 36 |
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| container_title | Mediterranean journal of mathematics |
| container_volume | 19 |
| creator | Lan, Enhao |
| description | In this paper, we study the following equations
0.1
i
ϕ
t
=
-
A
(
|
|
∇
ϕ
|
|
2
)
Δ
ϕ
-
|
ϕ
|
p
-
1
ϕ
,
t
>
0
,
x
∈
R
n
,
ϕ
(
x
,
0
)
=
ϕ
0
(
x
)
∈
H
1
(
R
n
)
,
where
n
≥
1
,
1
<
p
<
n
+
4
n
,
A
(
s
) is a function. Under suitable conditions on
A
(
s
), we use Lyapunov method to prove the orbital stability of standing wave for (
0.1
). |
| doi_str_mv | 10.1007/s00009-021-01969-1 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2622098976</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2622098976</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-69e699ef8e205ccd228270f0e1302e6d33fd1052c010161e0e6303631719bbe23</originalsourceid><addsrcrecordid>eNp9kE1OwzAQhS0EEqVwAVaRWAdm7MSpl1VVfkRFF4W1lTg2dRXi1k4X3XEH7sIFuAknwSUIdsxmRqP33mg-Qs4RLhGguAoQS6RAMQUUXKR4QAbIOaR5lmeHv3PGj8lJCCsAKpDRARnPfWW7skkWXVnZxna7xJnkwbWNbXXpk4Va-o_32rbP2n--vt1br5ZLZ0wy3WzLzro2nJIjUzZBn_30IXm6nj5ObtPZ_OZuMp6lihbQpVxoLoQ2I00hV6qmdBT3BjQyoJrXjJkaIacKEJCjBs0ZMM6wQFFVmrIhuehz195ttjp0cuW2vo0nJeWUghiJgkcV7VXKuxC8NnLt7UvpdxJB7lHJHpWMqOQ3KonRxHpTiOL9p3_R_7i-AJgcbCQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2622098976</pqid></control><display><type>article</type><title>Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations</title><source>SpringerLink Journals - AutoHoldings</source><creator>Lan, Enhao</creator><creatorcontrib>Lan, Enhao</creatorcontrib><description>In this paper, we study the following equations
0.1
i
ϕ
t
=
-
A
(
|
|
∇
ϕ
|
|
2
)
Δ
ϕ
-
|
ϕ
|
p
-
1
ϕ
,
t
>
0
,
x
∈
R
n
,
ϕ
(
x
,
0
)
=
ϕ
0
(
x
)
∈
H
1
(
R
n
)
,
where
n
≥
1
,
1
<
p
<
n
+
4
n
,
A
(
s
) is a function. Under suitable conditions on
A
(
s
), we use Lyapunov method to prove the orbital stability of standing wave for (
0.1
).</description><identifier>ISSN: 1660-5446</identifier><identifier>EISSN: 1660-5454</identifier><identifier>DOI: 10.1007/s00009-021-01969-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Orbital stability ; Standing waves</subject><ispartof>Mediterranean journal of mathematics, 2022-02, Vol.19 (1), Article 36</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-69e699ef8e205ccd228270f0e1302e6d33fd1052c010161e0e6303631719bbe23</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/s00009-021-01969-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00009-021-01969-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Lan, Enhao</creatorcontrib><title>Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations</title><title>Mediterranean journal of mathematics</title><addtitle>Mediterr. J. Math</addtitle><description>In this paper, we study the following equations
0.1
i
ϕ
t
=
-
A
(
|
|
∇
ϕ
|
|
2
)
Δ
ϕ
-
|
ϕ
|
p
-
1
ϕ
,
t
>
0
,
x
∈
R
n
,
ϕ
(
x
,
0
)
=
ϕ
0
(
x
)
∈
H
1
(
R
n
)
,
where
n
≥
1
,
1
<
p
<
n
+
4
n
,
A
(
s
) is a function. Under suitable conditions on
A
(
s
), we use Lyapunov method to prove the orbital stability of standing wave for (
0.1
).</description><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Orbital stability</subject><subject>Standing waves</subject><issn>1660-5446</issn><issn>1660-5454</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhS0EEqVwAVaRWAdm7MSpl1VVfkRFF4W1lTg2dRXi1k4X3XEH7sIFuAknwSUIdsxmRqP33mg-Qs4RLhGguAoQS6RAMQUUXKR4QAbIOaR5lmeHv3PGj8lJCCsAKpDRARnPfWW7skkWXVnZxna7xJnkwbWNbXXpk4Va-o_32rbP2n--vt1br5ZLZ0wy3WzLzro2nJIjUzZBn_30IXm6nj5ObtPZ_OZuMp6lihbQpVxoLoQ2I00hV6qmdBT3BjQyoJrXjJkaIacKEJCjBs0ZMM6wQFFVmrIhuehz195ttjp0cuW2vo0nJeWUghiJgkcV7VXKuxC8NnLt7UvpdxJB7lHJHpWMqOQ3KonRxHpTiOL9p3_R_7i-AJgcbCQ</recordid><startdate>20220201</startdate><enddate>20220201</enddate><creator>Lan, Enhao</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220201</creationdate><title>Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations</title><author>Lan, Enhao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-69e699ef8e205ccd228270f0e1302e6d33fd1052c010161e0e6303631719bbe23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Orbital stability</topic><topic>Standing waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lan, Enhao</creatorcontrib><collection>CrossRef</collection><jtitle>Mediterranean journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lan, Enhao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations</atitle><jtitle>Mediterranean journal of mathematics</jtitle><stitle>Mediterr. J. Math</stitle><date>2022-02-01</date><risdate>2022</risdate><volume>19</volume><issue>1</issue><artnum>36</artnum><issn>1660-5446</issn><eissn>1660-5454</eissn><abstract>In this paper, we study the following equations
0.1
i
ϕ
t
=
-
A
(
|
|
∇
ϕ
|
|
2
)
Δ
ϕ
-
|
ϕ
|
p
-
1
ϕ
,
t
>
0
,
x
∈
R
n
,
ϕ
(
x
,
0
)
=
ϕ
0
(
x
)
∈
H
1
(
R
n
)
,
where
n
≥
1
,
1
<
p
<
n
+
4
n
,
A
(
s
) is a function. Under suitable conditions on
A
(
s
), we use Lyapunov method to prove the orbital stability of standing wave for (
0.1
).</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00009-021-01969-1</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1660-5446 |
| ispartof | Mediterranean journal of mathematics, 2022-02, Vol.19 (1), Article 36 |
| issn | 1660-5446 1660-5454 |
| language | eng |
| recordid | cdi_proquest_journals_2622098976 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Mathematical analysis Mathematics Mathematics and Statistics Orbital stability Standing waves |
| title | Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations |
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