Multiplicity results for asymmetric boundary value problems with indefinite weights
We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form u″+f(t,u)=0, u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S108533750440102X |
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| _version_ | 1832553436266102784 |
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| author | Francesca Dalbono |
| author_facet | Francesca Dalbono |
| author_sort | Francesca Dalbono |
| collection | DOAJ |
| description | We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form u″+f(t,u)=0, u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues. |
| format | Article |
| id | doaj-art-ebf7b5de1b914ca2bbc4b3cff82978cb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ebf7b5de1b914ca2bbc4b3cff82978cb2025-02-03T05:54:06ZengWileyAbstract and Applied Analysis1085-33751687-04092004-01-0120041195797910.1155/S108533750440102XMultiplicity results for asymmetric boundary value problems with indefinite weightsFrancesca Dalbono0Dipartimento di Matematica, Facoltà di Scienze Matematiche Fisiche e Naturali, Università di Torino, Via Carlo Alberto, Torino 10 10123, ItalyWe prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form u″+f(t,u)=0, u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.http://dx.doi.org/10.1155/S108533750440102X |
| spellingShingle | Francesca Dalbono Multiplicity results for asymmetric boundary value problems with indefinite weights Abstract and Applied Analysis |
| title | Multiplicity results for asymmetric boundary value problems with indefinite weights |
| title_full | Multiplicity results for asymmetric boundary value problems with indefinite weights |
| title_fullStr | Multiplicity results for asymmetric boundary value problems with indefinite weights |
| title_full_unstemmed | Multiplicity results for asymmetric boundary value problems with indefinite weights |
| title_short | Multiplicity results for asymmetric boundary value problems with indefinite weights |
| title_sort | multiplicity results for asymmetric boundary value problems with indefinite weights |
| url | http://dx.doi.org/10.1155/S108533750440102X |
| work_keys_str_mv | AT francescadalbono multiplicityresultsforasymmetricboundaryvalueproblemswithindefiniteweights |