Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations
We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear operator. As a new auxiliary tool a limiting absorpti...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-08-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2019-2050 |
| _version_ | 1798043435079303168 |
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| author | Mandel Rainer |
| author_facet | Mandel Rainer |
| author_sort | Mandel Rainer |
| collection | DOAJ |
| description | We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear operator. As a new auxiliary tool a limiting absorption principle for the curl-curl operator is proved. |
| first_indexed | 2024-04-11T22:49:02Z |
| format | Article |
| id | doaj.art-7615ed6a480c4fc8aeb0408511c3b1e6 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-11T22:49:02Z |
| publishDate | 2019-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-7615ed6a480c4fc8aeb0408511c3b1e62022-12-22T03:58:39ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752019-08-0119356959310.1515/ans-2019-2050Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl EquationsMandel Rainer0Institute for Analysis, Karlsruhe Institute of Technology, Englerstraße 2, 76131Karlsruhe, GermanyWe obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear operator. As a new auxiliary tool a limiting absorption principle for the curl-curl operator is proved.https://doi.org/10.1515/ans-2019-2050nonlinear helmholtz equationscurl-curl equationslimiting absorption principlesherglotz waves35q60 35q61 35j91 |
| spellingShingle | Mandel Rainer Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations Advanced Nonlinear Studies nonlinear helmholtz equations curl-curl equations limiting absorption principles herglotz waves 35q60 35q61 35j91 |
| title | Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations |
| title_full | Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations |
| title_fullStr | Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations |
| title_full_unstemmed | Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations |
| title_short | Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations |
| title_sort | uncountably many solutions for nonlinear helmholtz and curl curl equations |
| topic | nonlinear helmholtz equations curl-curl equations limiting absorption principles herglotz waves 35q60 35q61 35j91 |
| url | https://doi.org/10.1515/ans-2019-2050 |
| work_keys_str_mv | AT mandelrainer uncountablymanysolutionsfornonlinearhelmholtzandcurlcurlequations |