A generalized Fucik type eigenvalue problem for p-Laplacian
In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional $p-$Laplace type differential equations \[ \left\{\begin{array}{lll} - (\varphi( u')) ' = \psi(u), \quad -T< x < T; \\ \quad u(-T)=0, \quad u(T)=0 \\ \end{array} \right.\ta...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2009-03-01
|
| 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=372 |
| _version_ | 1797830692997955584 |
|---|---|
| author | Yuanji Cheng |
| author_facet | Yuanji Cheng |
| author_sort | Yuanji Cheng |
| collection | DOAJ |
| description | In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional $p-$Laplace type differential equations
\[
\left\{\begin{array}{lll} - (\varphi( u')) ' = \psi(u), \quad -T< x < T; \\
\quad u(-T)=0, \quad u(T)=0 \\
\end{array} \right.\tag{*}
\]
where $\varphi (s) = \alpha s_+^{p-1} -\beta s_-^{p-1}, \psi (s) = \lambda s_+^{p-1} -\mu s_-^{p-1}, p >1.$ We obtain a explicit characterization of Fucik spectrum $(\alpha, \beta, \lambda, \mu),$ i.e., for which the (*) has a nontrivial solution. |
| first_indexed | 2024-04-09T13:41:16Z |
| format | Article |
| id | doaj.art-1d7909a537574552b32b2cbeb6b905a6 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:16Z |
| publishDate | 2009-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1d7909a537574552b32b2cbeb6b905a62023-05-09T07:52:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752009-03-012009181910.14232/ejqtde.2009.1.18372A generalized Fucik type eigenvalue problem for p-LaplacianYuanji Cheng0Malmö University, Malmö, SwedenIn this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional $p-$Laplace type differential equations \[ \left\{\begin{array}{lll} - (\varphi( u')) ' = \psi(u), \quad -T< x < T; \\ \quad u(-T)=0, \quad u(T)=0 \\ \end{array} \right.\tag{*} \] where $\varphi (s) = \alpha s_+^{p-1} -\beta s_-^{p-1}, \psi (s) = \lambda s_+^{p-1} -\mu s_-^{p-1}, p >1.$ We obtain a explicit characterization of Fucik spectrum $(\alpha, \beta, \lambda, \mu),$ i.e., for which the (*) has a nontrivial solution.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=372 |
| spellingShingle | Yuanji Cheng A generalized Fucik type eigenvalue problem for p-Laplacian Electronic Journal of Qualitative Theory of Differential Equations |
| title | A generalized Fucik type eigenvalue problem for p-Laplacian |
| title_full | A generalized Fucik type eigenvalue problem for p-Laplacian |
| title_fullStr | A generalized Fucik type eigenvalue problem for p-Laplacian |
| title_full_unstemmed | A generalized Fucik type eigenvalue problem for p-Laplacian |
| title_short | A generalized Fucik type eigenvalue problem for p-Laplacian |
| title_sort | generalized fucik type eigenvalue problem for p laplacian |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=372 |
| work_keys_str_mv | AT yuanjicheng ageneralizedfuciktypeeigenvalueproblemforplaplacian AT yuanjicheng generalizedfuciktypeeigenvalueproblemforplaplacian |