Spectrum of one dimensional p-Laplacian operator with indefinite weight
This paper is concerned with the nonlinear boundary eigenvalue problem $$-(|u'|^{p-2}u')'=\lambda m|u|^{p-2}u\qquad u \in I=]a,b[,\quad u(a)=u(b)=0,$$ where $p>1$, $\lambda$ is a real parameter, $m$ is an indefinite weight, and $a$, $b$ are real numbers. We prove there exists a uni...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2002-01-01
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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=143 |
| _version_ | 1797830806116237312 |
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| author | Mohammed Moussa A. Anane Omar Chakrone |
| author_facet | Mohammed Moussa A. Anane Omar Chakrone |
| author_sort | Mohammed Moussa |
| collection | DOAJ |
| description | This paper is concerned with the nonlinear boundary eigenvalue problem
$$-(|u'|^{p-2}u')'=\lambda m|u|^{p-2}u\qquad u \in I=]a,b[,\quad u(a)=u(b)=0,$$
where $p>1$, $\lambda$ is a real parameter, $m$ is an indefinite weight, and $a$, $b$ are real numbers. We prove there exists a unique sequence of eigenvalues for this problem. Each eigenvalue is simple and verifies the strict monotonicity property with respect to the weight $m$ and the domain $I$, the k-th eigenfunction, corresponding to the $k$-th eigenvalue, has exactly $k-1$ zeros in $(a,b)$. At the end, we give a simple variational formulation of eigenvalues. |
| first_indexed | 2024-04-09T13:41:58Z |
| format | Article |
| id | doaj.art-cde228db66cc4534bf4d5aa46060457c |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:58Z |
| publishDate | 2002-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-cde228db66cc4534bf4d5aa46060457c2023-05-09T07:52:57ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752002-01-0120021711110.14232/ejqtde.2002.1.17143Spectrum of one dimensional p-Laplacian operator with indefinite weightMohammed Moussa0A. Anane1Omar Chakrone2University Ibn Tofail, Kenitra, MoroccoUniversity Mohamed Ist, Oujda, MoroccoUniversity Mohamed Ist, Oujda, MoroccoThis paper is concerned with the nonlinear boundary eigenvalue problem $$-(|u'|^{p-2}u')'=\lambda m|u|^{p-2}u\qquad u \in I=]a,b[,\quad u(a)=u(b)=0,$$ where $p>1$, $\lambda$ is a real parameter, $m$ is an indefinite weight, and $a$, $b$ are real numbers. We prove there exists a unique sequence of eigenvalues for this problem. Each eigenvalue is simple and verifies the strict monotonicity property with respect to the weight $m$ and the domain $I$, the k-th eigenfunction, corresponding to the $k$-th eigenvalue, has exactly $k-1$ zeros in $(a,b)$. At the end, we give a simple variational formulation of eigenvalues.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=143 |
| spellingShingle | Mohammed Moussa A. Anane Omar Chakrone Spectrum of one dimensional p-Laplacian operator with indefinite weight Electronic Journal of Qualitative Theory of Differential Equations |
| title | Spectrum of one dimensional p-Laplacian operator with indefinite weight |
| title_full | Spectrum of one dimensional p-Laplacian operator with indefinite weight |
| title_fullStr | Spectrum of one dimensional p-Laplacian operator with indefinite weight |
| title_full_unstemmed | Spectrum of one dimensional p-Laplacian operator with indefinite weight |
| title_short | Spectrum of one dimensional p-Laplacian operator with indefinite weight |
| title_sort | spectrum of one dimensional p laplacian operator with indefinite weight |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=143 |
| work_keys_str_mv | AT mohammedmoussa spectrumofonedimensionalplaplacianoperatorwithindefiniteweight AT aanane spectrumofonedimensionalplaplacianoperatorwithindefiniteweight AT omarchakrone spectrumofonedimensionalplaplacianoperatorwithindefiniteweight |