Multiplicity and concentration results for a (p, q)-Laplacian problem in RN
In this paper, we study the multiplicity and concentration of positive solutions for the following ( p , q )-Laplacian problem: - Δ p u - Δ q u + V ( ε x ) | u | p - 2 u + | u | q - 2 u = f ( u ) in R N , u ∈ W 1 , p ( R N ) ∩ W 1 , q ( R N ) , u > 0 in R N , where ε > 0 is a small parameter,...
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| creator | Ambrosio, Vincenzo Repovš, Dušan |
| description | In this paper, we study the multiplicity and concentration of positive solutions for the following (
p
,
q
)-Laplacian problem:
-
Δ
p
u
-
Δ
q
u
+
V
(
ε
x
)
|
u
|
p
-
2
u
+
|
u
|
q
-
2
u
=
f
(
u
)
in
R
N
,
u
∈
W
1
,
p
(
R
N
)
∩
W
1
,
q
(
R
N
)
,
u
>
0
in
R
N
,
where
ε
>
0
is a small parameter,
1
<
p
<
q
<
N
,
Δ
r
u
=
div
(
|
∇
u
|
r
-
2
∇
u
)
, with
r
∈
{
p
,
q
}
, is the
r
-Laplacian operator,
V
:
R
N
→
R
is a continuous function satisfying the global Rabinowitz condition, and
f
:
R
→
R
is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik–Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where
V
attains its minimum for small
ε
. |
| doi_str_mv | 10.1007/s00033-020-01466-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_2478787841</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2478787841</sourcerecordid><originalsourceid>FETCH-LOGICAL-p727-fb1ca16254c462acdd09e1eb965db030df449c3b3f303d5ae2f30930d228d883</originalsourceid><addsrcrecordid>eNpFkMtKxDAUhoMoOI6-gKuAGwWjJ5c27VKG8QJVQd2HNEklQ007SWfh2_gsPpkZR5CzOBc-zg8fQqcUriiAvE4AwDkBBgSoKEsi99CMirzWwOt9NAMQgjAmi0N0lNIq45ICn6HmcdNPfuy98dMn1sFiMwTjwhT15IeAo0sZSLgbItb4fLz8_lpfkEaPvTZeBzzGoe3dB_YBvzwdo4NO98md_PU5er1dvi3uSfN897C4acgomSRdS42mJSuEESXTxlqoHXVtXRa2BQ62E6I2vOUdB24L7Vge6nxnrLJVxefobPc1Z683Lk1qNWxiyIGKCVltS9BM8R2VxujDu4v_FAW1laZ20lSWpn6lKcl_AJ9zXz0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2478787841</pqid></control><display><type>article</type><title>Multiplicity and concentration results for a (p, q)-Laplacian problem in RN</title><source>SpringerLink Journals - AutoHoldings</source><creator>Ambrosio, Vincenzo ; Repovš, Dušan</creator><creatorcontrib>Ambrosio, Vincenzo ; Repovš, Dušan</creatorcontrib><description>In this paper, we study the multiplicity and concentration of positive solutions for the following (
p
,
q
)-Laplacian problem:
-
Δ
p
u
-
Δ
q
u
+
V
(
ε
x
)
|
u
|
p
-
2
u
+
|
u
|
q
-
2
u
=
f
(
u
)
in
R
N
,
u
∈
W
1
,
p
(
R
N
)
∩
W
1
,
q
(
R
N
)
,
u
>
0
in
R
N
,
where
ε
>
0
is a small parameter,
1
<
p
<
q
<
N
,
Δ
r
u
=
div
(
|
∇
u
|
r
-
2
∇
u
)
, with
r
∈
{
p
,
q
}
, is the
r
-Laplacian operator,
V
:
R
N
→
R
is a continuous function satisfying the global Rabinowitz condition, and
f
:
R
→
R
is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik–Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where
V
attains its minimum for small
ε
.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-020-01466-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Continuity (mathematics) ; Engineering ; Mathematical Methods in Physics ; Operators (mathematics) ; Theoretical and Applied Mechanics ; Topology</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2021, Vol.72 (1)</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0003-3439-1428</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00033-020-01466-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-020-01466-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Ambrosio, Vincenzo</creatorcontrib><creatorcontrib>Repovš, Dušan</creatorcontrib><title>Multiplicity and concentration results for a (p, q)-Laplacian problem in RN</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>In this paper, we study the multiplicity and concentration of positive solutions for the following (
p
,
q
)-Laplacian problem:
-
Δ
p
u
-
Δ
q
u
+
V
(
ε
x
)
|
u
|
p
-
2
u
+
|
u
|
q
-
2
u
=
f
(
u
)
in
R
N
,
u
∈
W
1
,
p
(
R
N
)
∩
W
1
,
q
(
R
N
)
,
u
>
0
in
R
N
,
where
ε
>
0
is a small parameter,
1
<
p
<
q
<
N
,
Δ
r
u
=
div
(
|
∇
u
|
r
-
2
∇
u
)
, with
r
∈
{
p
,
q
}
, is the
r
-Laplacian operator,
V
:
R
N
→
R
is a continuous function satisfying the global Rabinowitz condition, and
f
:
R
→
R
is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik–Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where
V
attains its minimum for small
ε
.</description><subject>Continuity (mathematics)</subject><subject>Engineering</subject><subject>Mathematical Methods in Physics</subject><subject>Operators (mathematics)</subject><subject>Theoretical and Applied Mechanics</subject><subject>Topology</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkMtKxDAUhoMoOI6-gKuAGwWjJ5c27VKG8QJVQd2HNEklQ007SWfh2_gsPpkZR5CzOBc-zg8fQqcUriiAvE4AwDkBBgSoKEsi99CMirzWwOt9NAMQgjAmi0N0lNIq45ICn6HmcdNPfuy98dMn1sFiMwTjwhT15IeAo0sZSLgbItb4fLz8_lpfkEaPvTZeBzzGoe3dB_YBvzwdo4NO98md_PU5er1dvi3uSfN897C4acgomSRdS42mJSuEESXTxlqoHXVtXRa2BQ62E6I2vOUdB24L7Vge6nxnrLJVxefobPc1Z683Lk1qNWxiyIGKCVltS9BM8R2VxujDu4v_FAW1laZ20lSWpn6lKcl_AJ9zXz0</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Ambrosio, Vincenzo</creator><creator>Repovš, Dušan</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/><orcidid>https://orcid.org/0000-0003-3439-1428</orcidid></search><sort><creationdate>2021</creationdate><title>Multiplicity and concentration results for a (p, q)-Laplacian problem in RN</title><author>Ambrosio, Vincenzo ; Repovš, Dušan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p727-fb1ca16254c462acdd09e1eb965db030df449c3b3f303d5ae2f30930d228d883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Continuity (mathematics)</topic><topic>Engineering</topic><topic>Mathematical Methods in Physics</topic><topic>Operators (mathematics)</topic><topic>Theoretical and Applied Mechanics</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ambrosio, Vincenzo</creatorcontrib><creatorcontrib>Repovš, Dušan</creatorcontrib><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ambrosio, Vincenzo</au><au>Repovš, Dušan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiplicity and concentration results for a (p, q)-Laplacian problem in RN</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2021</date><risdate>2021</risdate><volume>72</volume><issue>1</issue><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>In this paper, we study the multiplicity and concentration of positive solutions for the following (
p
,
q
)-Laplacian problem:
-
Δ
p
u
-
Δ
q
u
+
V
(
ε
x
)
|
u
|
p
-
2
u
+
|
u
|
q
-
2
u
=
f
(
u
)
in
R
N
,
u
∈
W
1
,
p
(
R
N
)
∩
W
1
,
q
(
R
N
)
,
u
>
0
in
R
N
,
where
ε
>
0
is a small parameter,
1
<
p
<
q
<
N
,
Δ
r
u
=
div
(
|
∇
u
|
r
-
2
∇
u
)
, with
r
∈
{
p
,
q
}
, is the
r
-Laplacian operator,
V
:
R
N
→
R
is a continuous function satisfying the global Rabinowitz condition, and
f
:
R
→
R
is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik–Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where
V
attains its minimum for small
ε
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-020-01466-7</doi><orcidid>https://orcid.org/0000-0003-3439-1428</orcidid></addata></record> |
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| issn | 0044-2275 1420-9039 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Continuity (mathematics) Engineering Mathematical Methods in Physics Operators (mathematics) Theoretical and Applied Mechanics Topology |
| title | Multiplicity and concentration results for a (p, q)-Laplacian problem in RN |
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