On existence of multiple normalized solutions to a class of elliptic problems in whole RN
In this paper, we study the existence of multiple normalized solutions to the following class of elliptic problems - Δ u = λ u + h ( ϵ x ) f ( u ) , in R N , ∫ R N | u | 2 d x = a 2 , where a , ϵ > 0 , λ ∈ R is an unknown parameter that appears as a Lagrange multiplier, h : R N → [ 0 , ∞ ) is a c...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2022, Vol.73 (3) |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
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| creator | Alves, Claudianor O. |
| description | In this paper, we study the existence of multiple normalized solutions to the following class of elliptic problems
-
Δ
u
=
λ
u
+
h
(
ϵ
x
)
f
(
u
)
,
in
R
N
,
∫
R
N
|
u
|
2
d
x
=
a
2
,
where
a
,
ϵ
>
0
,
λ
∈
R
is an unknown parameter that appears as a Lagrange multiplier,
h
:
R
N
→
[
0
,
∞
)
is a continuous function, and
f
is continuous function with
L
2
-subcritical growth. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of
h
when
ϵ
is small enough. |
| doi_str_mv | 10.1007/s00033-022-01741-9 |
| format | Article |
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-
Δ
u
=
λ
u
+
h
(
ϵ
x
)
f
(
u
)
,
in
R
N
,
∫
R
N
|
u
|
2
d
x
=
a
2
,
where
a
,
ϵ
>
0
,
λ
∈
R
is an unknown parameter that appears as a Lagrange multiplier,
h
:
R
N
→
[
0
,
∞
)
is a continuous function, and
f
is continuous function with
L
2
-subcritical growth. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of
h
when
ϵ
is small enough.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-022-01741-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Continuity (mathematics) ; Engineering ; Lagrange multiplier ; Mathematical Methods in Physics ; Theoretical and Applied Mechanics</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2022, Vol.73 (3)</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-p729-d938a87d9d4b3275e1f81b16cf2aa6f4b46d1f3642c0623d52a88154111c6b253</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/s00033-022-01741-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-022-01741-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Alves, Claudianor O.</creatorcontrib><title>On existence of multiple normalized solutions to a class of elliptic problems in whole RN</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>In this paper, we study the existence of multiple normalized solutions to the following class of elliptic problems
-
Δ
u
=
λ
u
+
h
(
ϵ
x
)
f
(
u
)
,
in
R
N
,
∫
R
N
|
u
|
2
d
x
=
a
2
,
where
a
,
ϵ
>
0
,
λ
∈
R
is an unknown parameter that appears as a Lagrange multiplier,
h
:
R
N
→
[
0
,
∞
)
is a continuous function, and
f
is continuous function with
L
2
-subcritical growth. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of
h
when
ϵ
is small enough.</description><subject>Continuity (mathematics)</subject><subject>Engineering</subject><subject>Lagrange multiplier</subject><subject>Mathematical Methods in Physics</subject><subject>Theoretical and Applied Mechanics</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkEtLxDAUhYMoOI7-AVcB19F7k_SRpQy-YHBAZuMqpG2qGTJNbVoUf70ZK7g6m-_ce_gIuUS4RoDiJgKAEAw4Z4CFRKaOyAIlB6ZAqGOyAJCScV5kp-Qsxl3CCwSxIK-bjtovF0fb1ZaGlu4nP7reW9qFYW-8-7YNjcFPowtdpGOghtbexHhgrfeuH11N-yFU3u4jdR39fA-p_fJ8Tk5a46O9-Msl2d7fbVePbL15eFrdrllfcMUaJUpTFo1qZCXSPIttiRXmdcuNyVtZybzBVuSS15Bz0WTclCVmEhHrvOKZWJKr-Wza8DHZOOpdmIYufdQ8zxClEhkmSsxU7AfXvdnhn0LQB4V6VqiTQv2rUCvxA2v9Y34</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Alves, Claudianor O.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2022</creationdate><title>On existence of multiple normalized solutions to a class of elliptic problems in whole RN</title><author>Alves, Claudianor O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p729-d938a87d9d4b3275e1f81b16cf2aa6f4b46d1f3642c0623d52a88154111c6b253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Continuity (mathematics)</topic><topic>Engineering</topic><topic>Lagrange multiplier</topic><topic>Mathematical Methods in Physics</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alves, Claudianor O.</creatorcontrib><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alves, Claudianor O.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On existence of multiple normalized solutions to a class of elliptic problems in whole RN</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2022</date><risdate>2022</risdate><volume>73</volume><issue>3</issue><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>In this paper, we study the existence of multiple normalized solutions to the following class of elliptic problems
-
Δ
u
=
λ
u
+
h
(
ϵ
x
)
f
(
u
)
,
in
R
N
,
∫
R
N
|
u
|
2
d
x
=
a
2
,
where
a
,
ϵ
>
0
,
λ
∈
R
is an unknown parameter that appears as a Lagrange multiplier,
h
:
R
N
→
[
0
,
∞
)
is a continuous function, and
f
is continuous function with
L
2
-subcritical growth. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of
h
when
ϵ
is small enough.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-022-01741-9</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0044-2275 |
| ispartof | Zeitschrift für angewandte Mathematik und Physik, 2022, Vol.73 (3) |
| issn | 0044-2275 1420-9039 |
| language | eng |
| recordid | cdi_proquest_journals_2651149351 |
| source | SpringerLink Journals |
| subjects | Continuity (mathematics) Engineering Lagrange multiplier Mathematical Methods in Physics Theoretical and Applied Mechanics |
| title | On existence of multiple normalized solutions to a class of elliptic problems in whole RN |
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