Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations
In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation - ε 2 a + ε b ∫ R 3 | ∇ u | 2 d x Δ u + V ( x ) u = | u | p - 2 u , x ∈ R 3 , where a > 0 , b > 0 and 4 < p < 6 . Under only a local condition that V has a...
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| Veröffentlicht in: | The Journal of Geometric Analysis 2021-12, Vol.31 (12), p.12411-12445 |
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| container_title | The Journal of Geometric Analysis |
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| creator | Li, Quanqing Nie, Jianjun Wang, Wenbo Zhang, Jian |
| description | In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation
-
ε
2
a
+
ε
b
∫
R
3
|
∇
u
|
2
d
x
Δ
u
+
V
(
x
)
u
=
|
u
|
p
-
2
u
,
x
∈
R
3
,
where
a
>
0
,
b
>
0
and
4
<
p
<
6
. Under only a local condition that
V
has a local trapping potential well, when
ε
>
0
is sufficiently small, we construct the existence of a sequence of localized nodal solutions concentrating around the local minimum points of the potential function
V
by using variational method and penalization approach. Moreover, we regard
b
as a parameter and study the asymptotic behavior of the nodal solutions as
b
↘
0
, which reflects some relationship between
b
>
0
and
b
=
0
. |
| doi_str_mv | 10.1007/s12220-021-00722-0 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2580707677</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A707338911</galeid><sourcerecordid>A707338911</sourcerecordid><originalsourceid>FETCH-LOGICAL-c358t-8fdb04b06f0e994aac323e6fd1df70ccfc401c256178c17294ba26ba754ff7b3</originalsourceid><addsrcrecordid>eNp9kM9PwyAUxxujiXP6D3gi8Yw-aAvtcS7zR1z04A7eCKWwsXSlg844_3rZauLNcIBHPp_3Xr5Jck3glgDwu0AopYCBEhxLSjGcJCOS52Us6cdpfEMOmJWUnScXIawBMpZmfJSY2ZcNvW6VRrKt0STsN13veqvQvV7JT-s8cgbNnZKN_dY1enW1bNC7a3a9dW1AJgISTRsZwgF8sV6tVs4YvNh3Gs22O3nkLpMzI5ugr37vcbJ4mC2mT3j-9vg8ncyxSvOix4WpK8gqYAZ0WWZSqpSmmpma1IaDUkZlQBTNGeGFIpyWWSUpqyTPM2N4lY6Tm6Ft5912p0Mv1m7n2zhR0LwADpxxHqnbgVrKRgvbGtd7qeKp9cYq12pj4_8k0mlalIREgQ6C8i4Er43ovN1IvxcExCF_MeQvYv7imL-AKKWDFCLcLrX_2-Uf6wfHRIia</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2580707677</pqid></control><display><type>article</type><title>Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations</title><source>SpringerNature Journals</source><creator>Li, Quanqing ; Nie, Jianjun ; Wang, Wenbo ; Zhang, Jian</creator><creatorcontrib>Li, Quanqing ; Nie, Jianjun ; Wang, Wenbo ; Zhang, Jian</creatorcontrib><description>In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation
-
ε
2
a
+
ε
b
∫
R
3
|
∇
u
|
2
d
x
Δ
u
+
V
(
x
)
u
=
|
u
|
p
-
2
u
,
x
∈
R
3
,
where
a
>
0
,
b
>
0
and
4
<
p
<
6
. Under only a local condition that
V
has a local trapping potential well, when
ε
>
0
is sufficiently small, we construct the existence of a sequence of localized nodal solutions concentrating around the local minimum points of the potential function
V
by using variational method and penalization approach. Moreover, we regard
b
as a parameter and study the asymptotic behavior of the nodal solutions as
b
↘
0
, which reflects some relationship between
b
>
0
and
b
=
0
.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-021-00722-0</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 ; Mathematics ; Mathematics and Statistics</subject><ispartof>The Journal of Geometric Analysis, 2021-12, Vol.31 (12), p.12411-12445</ispartof><rights>Mathematica Josephina, Inc. 2021</rights><rights>COPYRIGHT 2021 Springer</rights><rights>Mathematica Josephina, Inc. 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-8fdb04b06f0e994aac323e6fd1df70ccfc401c256178c17294ba26ba754ff7b3</citedby><cites>FETCH-LOGICAL-c358t-8fdb04b06f0e994aac323e6fd1df70ccfc401c256178c17294ba26ba754ff7b3</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/s12220-021-00722-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-021-00722-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Li, Quanqing</creatorcontrib><creatorcontrib>Nie, Jianjun</creatorcontrib><creatorcontrib>Wang, Wenbo</creatorcontrib><creatorcontrib>Zhang, Jian</creatorcontrib><title>Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation
-
ε
2
a
+
ε
b
∫
R
3
|
∇
u
|
2
d
x
Δ
u
+
V
(
x
)
u
=
|
u
|
p
-
2
u
,
x
∈
R
3
,
where
a
>
0
,
b
>
0
and
4
<
p
<
6
. Under only a local condition that
V
has a local trapping potential well, when
ε
>
0
is sufficiently small, we construct the existence of a sequence of localized nodal solutions concentrating around the local minimum points of the potential function
V
by using variational method and penalization approach. Moreover, we regard
b
as a parameter and study the asymptotic behavior of the nodal solutions as
b
↘
0
, which reflects some relationship between
b
>
0
and
b
=
0
.</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>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM9PwyAUxxujiXP6D3gi8Yw-aAvtcS7zR1z04A7eCKWwsXSlg844_3rZauLNcIBHPp_3Xr5Jck3glgDwu0AopYCBEhxLSjGcJCOS52Us6cdpfEMOmJWUnScXIawBMpZmfJSY2ZcNvW6VRrKt0STsN13veqvQvV7JT-s8cgbNnZKN_dY1enW1bNC7a3a9dW1AJgISTRsZwgF8sV6tVs4YvNh3Gs22O3nkLpMzI5ugr37vcbJ4mC2mT3j-9vg8ncyxSvOix4WpK8gqYAZ0WWZSqpSmmpma1IaDUkZlQBTNGeGFIpyWWSUpqyTPM2N4lY6Tm6Ft5912p0Mv1m7n2zhR0LwADpxxHqnbgVrKRgvbGtd7qeKp9cYq12pj4_8k0mlalIREgQ6C8i4Er43ovN1IvxcExCF_MeQvYv7imL-AKKWDFCLcLrX_2-Uf6wfHRIia</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Li, Quanqing</creator><creator>Nie, Jianjun</creator><creator>Wang, Wenbo</creator><creator>Zhang, Jian</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope></search><sort><creationdate>20211201</creationdate><title>Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations</title><author>Li, Quanqing ; Nie, Jianjun ; Wang, Wenbo ; Zhang, Jian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-8fdb04b06f0e994aac323e6fd1df70ccfc401c256178c17294ba26ba754ff7b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</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>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Quanqing</creatorcontrib><creatorcontrib>Nie, Jianjun</creatorcontrib><creatorcontrib>Wang, Wenbo</creatorcontrib><creatorcontrib>Zhang, Jian</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Quanqing</au><au>Nie, Jianjun</au><au>Wang, Wenbo</au><au>Zhang, Jian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>31</volume><issue>12</issue><spage>12411</spage><epage>12445</epage><pages>12411-12445</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation
-
ε
2
a
+
ε
b
∫
R
3
|
∇
u
|
2
d
x
Δ
u
+
V
(
x
)
u
=
|
u
|
p
-
2
u
,
x
∈
R
3
,
where
a
>
0
,
b
>
0
and
4
<
p
<
6
. Under only a local condition that
V
has a local trapping potential well, when
ε
>
0
is sufficiently small, we construct the existence of a sequence of localized nodal solutions concentrating around the local minimum points of the potential function
V
by using variational method and penalization approach. Moreover, we regard
b
as a parameter and study the asymptotic behavior of the nodal solutions as
b
↘
0
, which reflects some relationship between
b
>
0
and
b
=
0
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-021-00722-0</doi><tpages>35</tpages></addata></record> |
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| identifier | ISSN: 1050-6926 |
| ispartof | The Journal of Geometric Analysis, 2021-12, Vol.31 (12), p.12411-12445 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_proquest_journals_2580707677 |
| source | SpringerNature Journals |
| 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 Mathematics Mathematics and Statistics |
| title | Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations |
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