Hamiltonian systems involving exponential growth in R2 with general nonlinearities
In this work, we establish the existence of ground state solution for Hamiltonian systems of the form - Δ u + V ( x ) u = H v ( x , u , v ) , x ∈ R 2 , - Δ v + V ( x ) v = H u ( x , u , v ) , x ∈ R 2 , where V ∈ C ( R 2 , ( 0 , ∞ ) ) and H ∈ C 1 ( R 2 × R 2 , R ) is allowed to have an exponential gr...
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| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (1) |
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| container_title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas |
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| creator | Severo, Uberlandio B. Souza, Manassés de Menezes, Marta |
| description | In this work, we establish the existence of ground state solution for Hamiltonian systems of the form
-
Δ
u
+
V
(
x
)
u
=
H
v
(
x
,
u
,
v
)
,
x
∈
R
2
,
-
Δ
v
+
V
(
x
)
v
=
H
u
(
x
,
u
,
v
)
,
x
∈
R
2
,
where
V
∈
C
(
R
2
,
(
0
,
∞
)
)
and
H
∈
C
1
(
R
2
×
R
2
,
R
)
is allowed to have an exponential growth with respect to the Trudinger–Moser inequality. We study the case where
V
and
H
are periodic or asymptotically periodic. In the proof of the main results, we have used a reduction method involving the generalized Nehari manifold and also a linking theorem. In our approach, as we deal with general nonlinearities, it was necessary to obtain a new version of the Trudinger–Moser inequality. |
| doi_str_mv | 10.1007/s13398-023-01542-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_2910501930</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2910501930</sourcerecordid><originalsourceid>FETCH-LOGICAL-p157t-6a4fedfd475ad83357e337dec9db786878b5f5f2fcba66467a88c87a52f39a8c3</originalsourceid><addsrcrecordid>eNpFkEFLAzEQhYMoWGr_gKcFz9FkZ7PJHqWoFQpC0XNId5Oask3WJG3135t2BecyD-YxM-9D6JaSe0oIf4gUoBGYlIAJZVWJ4QJNKOMNpoywy7MWmAOBazSLcUtyAa0E4RO0Wqid7ZN3Vrki_sSkd7Gw7uD7g3WbQn8P3mmXrOqLTfDH9JmHxaosjjbLjXY65InzrrdOq2CT1fEGXRnVRz3761P08fz0Pl_g5dvL6_xxiYf8T8K1qozuTFdxpjoBwLgG4J1um27NRS24WDPDTGnatarrquZKiFZwxUoDjRItTNHduHcI_muvY5Jbvw8un5RlQwkjtMmRpwhGVxxCTqTDv4sSeeInR34y85NnfhLgFzlrZH0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2910501930</pqid></control><display><type>article</type><title>Hamiltonian systems involving exponential growth in R2 with general nonlinearities</title><source>SpringerLink Journals - AutoHoldings</source><creator>Severo, Uberlandio B. ; Souza, Manassés de ; Menezes, Marta</creator><creatorcontrib>Severo, Uberlandio B. ; Souza, Manassés de ; Menezes, Marta</creatorcontrib><description>In this work, we establish the existence of ground state solution for Hamiltonian systems of the form
-
Δ
u
+
V
(
x
)
u
=
H
v
(
x
,
u
,
v
)
,
x
∈
R
2
,
-
Δ
v
+
V
(
x
)
v
=
H
u
(
x
,
u
,
v
)
,
x
∈
R
2
,
where
V
∈
C
(
R
2
,
(
0
,
∞
)
)
and
H
∈
C
1
(
R
2
×
R
2
,
R
)
is allowed to have an exponential growth with respect to the Trudinger–Moser inequality. We study the case where
V
and
H
are periodic or asymptotically periodic. In the proof of the main results, we have used a reduction method involving the generalized Nehari manifold and also a linking theorem. In our approach, as we deal with general nonlinearities, it was necessary to obtain a new version of the Trudinger–Moser inequality.</description><identifier>ISSN: 1578-7303</identifier><identifier>EISSN: 1579-1505</identifier><identifier>DOI: 10.1007/s13398-023-01542-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Hamiltonian functions ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Original Paper ; Theoretical</subject><ispartof>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (1)</ispartof><rights>The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p157t-6a4fedfd475ad83357e337dec9db786878b5f5f2fcba66467a88c87a52f39a8c3</cites><orcidid>0000-0003-4984-1858</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/s13398-023-01542-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13398-023-01542-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Severo, Uberlandio B.</creatorcontrib><creatorcontrib>Souza, Manassés de</creatorcontrib><creatorcontrib>Menezes, Marta</creatorcontrib><title>Hamiltonian systems involving exponential growth in R2 with general nonlinearities</title><title>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</title><addtitle>Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat</addtitle><description>In this work, we establish the existence of ground state solution for Hamiltonian systems of the form
-
Δ
u
+
V
(
x
)
u
=
H
v
(
x
,
u
,
v
)
,
x
∈
R
2
,
-
Δ
v
+
V
(
x
)
v
=
H
u
(
x
,
u
,
v
)
,
x
∈
R
2
,
where
V
∈
C
(
R
2
,
(
0
,
∞
)
)
and
H
∈
C
1
(
R
2
×
R
2
,
R
)
is allowed to have an exponential growth with respect to the Trudinger–Moser inequality. We study the case where
V
and
H
are periodic or asymptotically periodic. In the proof of the main results, we have used a reduction method involving the generalized Nehari manifold and also a linking theorem. In our approach, as we deal with general nonlinearities, it was necessary to obtain a new version of the Trudinger–Moser inequality.</description><subject>Applications of Mathematics</subject><subject>Hamiltonian functions</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Original Paper</subject><subject>Theoretical</subject><issn>1578-7303</issn><issn>1579-1505</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNpFkEFLAzEQhYMoWGr_gKcFz9FkZ7PJHqWoFQpC0XNId5Oask3WJG3135t2BecyD-YxM-9D6JaSe0oIf4gUoBGYlIAJZVWJ4QJNKOMNpoywy7MWmAOBazSLcUtyAa0E4RO0Wqid7ZN3Vrki_sSkd7Gw7uD7g3WbQn8P3mmXrOqLTfDH9JmHxaosjjbLjXY65InzrrdOq2CT1fEGXRnVRz3761P08fz0Pl_g5dvL6_xxiYf8T8K1qozuTFdxpjoBwLgG4J1um27NRS24WDPDTGnatarrquZKiFZwxUoDjRItTNHduHcI_muvY5Jbvw8un5RlQwkjtMmRpwhGVxxCTqTDv4sSeeInR34y85NnfhLgFzlrZH0</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Severo, Uberlandio B.</creator><creator>Souza, Manassés de</creator><creator>Menezes, Marta</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-4984-1858</orcidid></search><sort><creationdate>2024</creationdate><title>Hamiltonian systems involving exponential growth in R2 with general nonlinearities</title><author>Severo, Uberlandio B. ; Souza, Manassés de ; Menezes, Marta</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-6a4fedfd475ad83357e337dec9db786878b5f5f2fcba66467a88c87a52f39a8c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Applications of Mathematics</topic><topic>Hamiltonian functions</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Original Paper</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Severo, Uberlandio B.</creatorcontrib><creatorcontrib>Souza, Manassés de</creatorcontrib><creatorcontrib>Menezes, Marta</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Severo, Uberlandio B.</au><au>Souza, Manassés de</au><au>Menezes, Marta</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hamiltonian systems involving exponential growth in R2 with general nonlinearities</atitle><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle><stitle>Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat</stitle><date>2024</date><risdate>2024</risdate><volume>118</volume><issue>1</issue><issn>1578-7303</issn><eissn>1579-1505</eissn><abstract>In this work, we establish the existence of ground state solution for Hamiltonian systems of the form
-
Δ
u
+
V
(
x
)
u
=
H
v
(
x
,
u
,
v
)
,
x
∈
R
2
,
-
Δ
v
+
V
(
x
)
v
=
H
u
(
x
,
u
,
v
)
,
x
∈
R
2
,
where
V
∈
C
(
R
2
,
(
0
,
∞
)
)
and
H
∈
C
1
(
R
2
×
R
2
,
R
)
is allowed to have an exponential growth with respect to the Trudinger–Moser inequality. We study the case where
V
and
H
are periodic or asymptotically periodic. In the proof of the main results, we have used a reduction method involving the generalized Nehari manifold and also a linking theorem. In our approach, as we deal with general nonlinearities, it was necessary to obtain a new version of the Trudinger–Moser inequality.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s13398-023-01542-3</doi><orcidid>https://orcid.org/0000-0003-4984-1858</orcidid></addata></record> |
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| ispartof | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (1) |
| issn | 1578-7303 1579-1505 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Hamiltonian functions Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonlinearity Original Paper Theoretical |
| title | Hamiltonian systems involving exponential growth in R2 with general nonlinearities |
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