Global bifurcations of critical orbits of G -invariant strongly indefinite functionals
Let H be a separable Hilbert space which is an orthogonal representation of a compact Lie group G and let Φ : H → R be a G -invariant strongly indefinite functional of the class C 1 . To study critical orbits of Φ we have defined the degree for G -invariant strongly indefinite functionals, which is...
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| Veröffentlicht in: | Nonlinear analysis 2011-03, Vol.74 (5), p.1823-1834 |
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| container_title | Nonlinear analysis |
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| creator | Gołȩbiewska, Anna Rybicki, Sławomir |
| description | Let
H
be a separable Hilbert space which is an orthogonal representation of a compact Lie group
G
and let
Φ
:
H
→
R
be a
G
-invariant strongly indefinite functional of the class
C
1
. To study critical orbits of
Φ
we have defined the degree for
G
-invariant strongly indefinite functionals, which is an element of the Euler ring
U
(
G
)
. Using this degree we have formulated the Rabinowitz alternative for
G
-invariant strongly indefinite functionals. The abstract results are applied to the study of global bifurcations of weak solutions of non-cooperative systems of elliptic differential equations. |
| doi_str_mv | 10.1016/j.na.2010.10.055 |
| format | Article |
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H
be a separable Hilbert space which is an orthogonal representation of a compact Lie group
G
and let
Φ
:
H
→
R
be a
G
-invariant strongly indefinite functional of the class
C
1
. To study critical orbits of
Φ
we have defined the degree for
G
-invariant strongly indefinite functionals, which is an element of the Euler ring
U
(
G
)
. Using this degree we have formulated the Rabinowitz alternative for
G
-invariant strongly indefinite functionals. The abstract results are applied to the study of global bifurcations of weak solutions of non-cooperative systems of elliptic differential equations.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2010.10.055</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Bifurcations ; Elliptic differential equations ; Exact sciences and technology ; Functional analysis ; Functionals ; Geometry ; Global bifurcation of critical orbits ; Group theory ; Hilbert space ; Lie groups ; Mathematical analysis ; Mathematics ; Non-cooperative elliptic systems ; Nonlinear algebraic and transcendental equations ; Nonlinearity ; Numerical analysis ; Numerical analysis. Scientific computation ; Orbits ; Representations ; Sciences and techniques of general use ; Strongly indefinite functionals ; Topological groups, lie groups</subject><ispartof>Nonlinear analysis, 2011-03, Vol.74 (5), p.1823-1834</ispartof><rights>2010 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c356t-13470ce1738caec8448e9a1d98f81ad7682ea7ce09d134edf2d10ba3d64c79e83</citedby><cites>FETCH-LOGICAL-c356t-13470ce1738caec8448e9a1d98f81ad7682ea7ce09d134edf2d10ba3d64c79e83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2010.10.055$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23853264$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Gołȩbiewska, Anna</creatorcontrib><creatorcontrib>Rybicki, Sławomir</creatorcontrib><title>Global bifurcations of critical orbits of G -invariant strongly indefinite functionals</title><title>Nonlinear analysis</title><description>Let
H
be a separable Hilbert space which is an orthogonal representation of a compact Lie group
G
and let
Φ
:
H
→
R
be a
G
-invariant strongly indefinite functional of the class
C
1
. To study critical orbits of
Φ
we have defined the degree for
G
-invariant strongly indefinite functionals, which is an element of the Euler ring
U
(
G
)
. Using this degree we have formulated the Rabinowitz alternative for
G
-invariant strongly indefinite functionals. The abstract results are applied to the study of global bifurcations of weak solutions of non-cooperative systems of elliptic differential equations.</description><subject>Bifurcations</subject><subject>Elliptic differential equations</subject><subject>Exact sciences and technology</subject><subject>Functional analysis</subject><subject>Functionals</subject><subject>Geometry</subject><subject>Global bifurcation of critical orbits</subject><subject>Group theory</subject><subject>Hilbert space</subject><subject>Lie groups</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Non-cooperative elliptic systems</subject><subject>Nonlinear algebraic and transcendental equations</subject><subject>Nonlinearity</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Orbits</subject><subject>Representations</subject><subject>Sciences and techniques of general use</subject><subject>Strongly indefinite functionals</subject><subject>Topological groups, lie groups</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PAzEMhiMEEqWwM96CmK4kl8tdyoYQFKRKLIDYojRxkKtrUpIUiX9P-iE2Jsv249f2S8gloxNGWXeznHg9aegunVAhjsiIyZ7XomHimIwo75patN3HKTlLaUkpZT3vRuR9NoSFHqoFuk00OmPwqQquMhEzmtIIcYF5V5pVNfpvHVH7XKUcg_8cfir0Fhx6zFC5jTdbAT2kc3LiSoCLQxyTt8eH1_unev4ye76_m9eGiy7XjLc9NVBOkUaDkW0rYaqZnUonmbZ9JxvQvQE6tQUF6xrL6EJz27Wmn4LkY3K9113H8LWBlNUKk4Fh0B7CJikpRM-46Gkh6Z40MaQUwal1xJWOP4pRtXVQLZXXauvgtlIcLCNXB3GdihUuam8w_c01XAredG3hbvcclE-_EaJKBsEbsBjBZGUD_r_kF9EDhks</recordid><startdate>20110301</startdate><enddate>20110301</enddate><creator>Gołȩbiewska, Anna</creator><creator>Rybicki, Sławomir</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><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></search><sort><creationdate>20110301</creationdate><title>Global bifurcations of critical orbits of G -invariant strongly indefinite functionals</title><author>Gołȩbiewska, Anna ; Rybicki, Sławomir</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c356t-13470ce1738caec8448e9a1d98f81ad7682ea7ce09d134edf2d10ba3d64c79e83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Bifurcations</topic><topic>Elliptic differential equations</topic><topic>Exact sciences and technology</topic><topic>Functional analysis</topic><topic>Functionals</topic><topic>Geometry</topic><topic>Global bifurcation of critical orbits</topic><topic>Group theory</topic><topic>Hilbert space</topic><topic>Lie groups</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Non-cooperative elliptic systems</topic><topic>Nonlinear algebraic and transcendental equations</topic><topic>Nonlinearity</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Orbits</topic><topic>Representations</topic><topic>Sciences and techniques of general use</topic><topic>Strongly indefinite functionals</topic><topic>Topological groups, lie groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gołȩbiewska, Anna</creatorcontrib><creatorcontrib>Rybicki, Sławomir</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><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>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gołȩbiewska, Anna</au><au>Rybicki, Sławomir</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global bifurcations of critical orbits of G -invariant strongly indefinite functionals</atitle><jtitle>Nonlinear analysis</jtitle><date>2011-03-01</date><risdate>2011</risdate><volume>74</volume><issue>5</issue><spage>1823</spage><epage>1834</epage><pages>1823-1834</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>Let
H
be a separable Hilbert space which is an orthogonal representation of a compact Lie group
G
and let
Φ
:
H
→
R
be a
G
-invariant strongly indefinite functional of the class
C
1
. To study critical orbits of
Φ
we have defined the degree for
G
-invariant strongly indefinite functionals, which is an element of the Euler ring
U
(
G
)
. Using this degree we have formulated the Rabinowitz alternative for
G
-invariant strongly indefinite functionals. The abstract results are applied to the study of global bifurcations of weak solutions of non-cooperative systems of elliptic differential equations.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2010.10.055</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2011-03, Vol.74 (5), p.1823-1834 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_855713570 |
| source | Elsevier ScienceDirect Journals |
| subjects | Bifurcations Elliptic differential equations Exact sciences and technology Functional analysis Functionals Geometry Global bifurcation of critical orbits Group theory Hilbert space Lie groups Mathematical analysis Mathematics Non-cooperative elliptic systems Nonlinear algebraic and transcendental equations Nonlinearity Numerical analysis Numerical analysis. Scientific computation Orbits Representations Sciences and techniques of general use Strongly indefinite functionals Topological groups, lie groups |
| title | Global bifurcations of critical orbits of G -invariant strongly indefinite functionals |
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