Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One
This paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem −u″(t)=λu(t)+g(t,u(t)), u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/284696 |
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| _version_ | 1832561103883730944 |
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| author | José L. Gámez Juan F. Ruiz-Hidalgo |
| author_facet | José L. Gámez Juan F. Ruiz-Hidalgo |
| author_sort | José L. Gámez |
| collection | DOAJ |
| description | This paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem −u″(t)=λu(t)+g(t,u(t)), u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g we obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems. |
| format | Article |
| id | doaj-art-951f5bd9c6c342189ce9ec857051a2e6 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-951f5bd9c6c342189ce9ec857051a2e62025-02-03T01:25:58ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/284696284696Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension OneJosé L. Gámez0Juan F. Ruiz-Hidalgo1Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, SpainDepartamento de Didáctica de la Matemática, Facultad de Ciencias de la Educación, Campus de Cartuja, Universidad de Granada, 18071 Granada, SpainThis paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem −u″(t)=λu(t)+g(t,u(t)), u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g we obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems.http://dx.doi.org/10.1155/2012/284696 |
| spellingShingle | José L. Gámez Juan F. Ruiz-Hidalgo Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One Journal of Function Spaces and Applications |
| title | Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One |
| title_full | Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One |
| title_fullStr | Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One |
| title_full_unstemmed | Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One |
| title_short | Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One |
| title_sort | bifurcation from infinity and resonance results at high eigenvalues in dimension one |
| url | http://dx.doi.org/10.1155/2012/284696 |
| work_keys_str_mv | AT joselgamez bifurcationfrominfinityandresonanceresultsathigheigenvaluesindimensionone AT juanfruizhidalgo bifurcationfrominfinityandresonanceresultsathigheigenvaluesindimensionone |