Fučík spectra for vector equations
Let $L:\hbox{dom} L\subset L^2(\Omega;R^N)\rightarrow L^2(\Omega;R^N)$ be a linear operator, $\Omega$ being open and bounded in $R^M$. The aim of this paper is to study the Fu\v c\'\i k spectrum for vector problems of the form $Lu=\alpha Au^+ -\beta Au^-$, where $A$ is an $N\times N$ matrix, $\...
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| Format: | Article |
| Language: | English |
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University of Szeged
2000-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=77 |
| _version_ | 1797830789264572416 |
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| author | Christian Fabry |
| author_facet | Christian Fabry |
| author_sort | Christian Fabry |
| collection | DOAJ |
| description | Let $L:\hbox{dom} L\subset L^2(\Omega;R^N)\rightarrow L^2(\Omega;R^N)$ be a linear operator, $\Omega$ being open and bounded in $R^M$. The aim of this paper is to study the Fu\v c\'\i k spectrum for vector problems of the form $Lu=\alpha Au^+ -\beta Au^-$, where $A$ is an $N\times N$ matrix, $\alpha, \beta$ are real numbers, $u^+$ a vector defined componentwise by $(u^+)_i=\max\{u_i,0\}$, $u^-$ being defined similarly. With $\lambda^*$ an eigenvalue for the problem $Lu=\lambda Au$, we describe (locally) curves in the Fučík spectrum passing through the point $(\lambda^*,\lambda^*)$, distinguishing different cases illustrated by examples, for which Fučík curves have been computed numerically. |
| first_indexed | 2024-04-09T13:42:47Z |
| format | Article |
| id | doaj.art-85ddc12466f94f46a20e6e14a15d5690 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:42:47Z |
| publishDate | 2000-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-85ddc12466f94f46a20e6e14a15d56902023-05-09T07:52:56ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752000-01-012000712410.14232/ejqtde.2000.1.777Fučík spectra for vector equationsChristian Fabry0Catholic University of Louvain, BelgiumLet $L:\hbox{dom} L\subset L^2(\Omega;R^N)\rightarrow L^2(\Omega;R^N)$ be a linear operator, $\Omega$ being open and bounded in $R^M$. The aim of this paper is to study the Fu\v c\'\i k spectrum for vector problems of the form $Lu=\alpha Au^+ -\beta Au^-$, where $A$ is an $N\times N$ matrix, $\alpha, \beta$ are real numbers, $u^+$ a vector defined componentwise by $(u^+)_i=\max\{u_i,0\}$, $u^-$ being defined similarly. With $\lambda^*$ an eigenvalue for the problem $Lu=\lambda Au$, we describe (locally) curves in the Fučík spectrum passing through the point $(\lambda^*,\lambda^*)$, distinguishing different cases illustrated by examples, for which Fučík curves have been computed numerically.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=77 |
| spellingShingle | Christian Fabry Fučík spectra for vector equations Electronic Journal of Qualitative Theory of Differential Equations |
| title | Fučík spectra for vector equations |
| title_full | Fučík spectra for vector equations |
| title_fullStr | Fučík spectra for vector equations |
| title_full_unstemmed | Fučík spectra for vector equations |
| title_short | Fučík spectra for vector equations |
| title_sort | fucik spectra for vector equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=77 |
| work_keys_str_mv | AT christianfabry fucikspectraforvectorequations |