A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities
This paper considers a class of degenerate quasilinear elliptic equations with discontinuous nonlinearities. The existence of positive weak solutions and S-solutions is discussed using variational methods. The results assert that the ( λ , a ) -space of the parameters involved is divided into three...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2023-04, Vol.62 (3), Article 91 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Santos, Jefferson Abrantes Pontes, Pedro F. Silva Soares, Sergio H. Monari |
| description | This paper considers a class of degenerate quasilinear elliptic equations with discontinuous nonlinearities. The existence of positive weak solutions and S-solutions is discussed using variational methods. The results assert that the
(
λ
,
a
)
-space of the parameters involved is divided into three regions - no solution, at least one S-solution, and at least two weak solutions (one is S-solution among them), in each region respectively. The regions are separated by a continuous, nondecreasing curve and line segment. Further, there exists an S-solution at each point on the separating curve. |
| doi_str_mv | 10.1007/s00526-023-02437-2 |
| format | Article |
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(
λ
,
a
)
-space of the parameters involved is divided into three regions - no solution, at least one S-solution, and at least two weak solutions (one is S-solution among them), in each region respectively. The regions are separated by a continuous, nondecreasing curve and line segment. Further, there exists an S-solution at each point on the separating curve.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-023-02437-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of Variations and Optimal Control; Optimization ; Control ; Eigenvalues ; Elliptic functions ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Systems Theory ; Theoretical ; Variational methods</subject><ispartof>Calculus of variations and partial differential equations, 2023-04, Vol.62 (3), Article 91</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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-c200t-5705a230e2d7d0c97987edd5c05ee311a5132068ec9ff0a955d625358e9ef9b63</cites><orcidid>0000-0002-2156-0889</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/s00526-023-02437-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-023-02437-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Santos, Jefferson Abrantes</creatorcontrib><creatorcontrib>Pontes, Pedro F. Silva</creatorcontrib><creatorcontrib>Soares, Sergio H. Monari</creatorcontrib><title>A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>This paper considers a class of degenerate quasilinear elliptic equations with discontinuous nonlinearities. The existence of positive weak solutions and S-solutions is discussed using variational methods. The results assert that the
(
λ
,
a
)
-space of the parameters involved is divided into three regions - no solution, at least one S-solution, and at least two weak solutions (one is S-solution among them), in each region respectively. The regions are separated by a continuous, nondecreasing curve and line segment. Further, there exists an S-solution at each point on the separating curve.</description><subject>Analysis</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Eigenvalues</subject><subject>Elliptic functions</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Systems Theory</subject><subject>Theoretical</subject><subject>Variational methods</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKAzEQhoMoWKsv4CngeXWSbDabYylqhYIXPYd0d7ambJM22VV8e6MrePMwDAzfPzN8hFwzuGUA6i4BSF4VwEWuUqiCn5AZKwUvoBbylMxAl2XBq0qfk4uUdgBM1rycEbug2z5sbE8jprEfaBcitbTFLXqMdkB6HG1yvfNoI0WXx--2H5EeYtj0uKcfbnijrUtN8IPzYxgT9cFPvBscpkty1tk-4dVvn5PXh_uX5apYPz8-LRfrouEAQyEVSMsFIG9VC41WulbYtrIBiSgYs5IJDlWNje46sFrKtuJSyBo1dnpTiTm5mfbmz44jpsHswhh9Pmm4UiA4k5XIFJ-oJoaUInbmEN3exk_DwHyrNJNKk1WaH5WG55CYQinDfovxb_U_qS_-enfi</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Santos, Jefferson Abrantes</creator><creator>Pontes, Pedro F. Silva</creator><creator>Soares, Sergio H. Monari</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0002-2156-0889</orcidid></search><sort><creationdate>20230401</creationdate><title>A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities</title><author>Santos, Jefferson Abrantes ; Pontes, Pedro F. Silva ; Soares, Sergio H. Monari</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-5705a230e2d7d0c97987edd5c05ee311a5132068ec9ff0a955d625358e9ef9b63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Eigenvalues</topic><topic>Elliptic functions</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Systems Theory</topic><topic>Theoretical</topic><topic>Variational methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Santos, Jefferson Abrantes</creatorcontrib><creatorcontrib>Pontes, Pedro F. Silva</creatorcontrib><creatorcontrib>Soares, Sergio H. Monari</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Santos, Jefferson Abrantes</au><au>Pontes, Pedro F. Silva</au><au>Soares, Sergio H. Monari</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>62</volume><issue>3</issue><artnum>91</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>This paper considers a class of degenerate quasilinear elliptic equations with discontinuous nonlinearities. The existence of positive weak solutions and S-solutions is discussed using variational methods. The results assert that the
(
λ
,
a
)
-space of the parameters involved is divided into three regions - no solution, at least one S-solution, and at least two weak solutions (one is S-solution among them), in each region respectively. The regions are separated by a continuous, nondecreasing curve and line segment. Further, there exists an S-solution at each point on the separating curve.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-023-02437-2</doi><orcidid>https://orcid.org/0000-0002-2156-0889</orcidid></addata></record> |
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| ispartof | Calculus of variations and partial differential equations, 2023-04, Vol.62 (3), Article 91 |
| issn | 0944-2669 1432-0835 |
| language | eng |
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| subjects | Analysis Calculus of Variations and Optimal Control Optimization Control Eigenvalues Elliptic functions Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonlinearity Systems Theory Theoretical Variational methods |
| title | A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities |
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