Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight
This paper is concerned with the global behavior of components of positive radial solutions for the quasilinear elliptic problem with indefinite weight \begin{equation*} \begin{aligned} &\text{div}(\varphi_p(\nabla u))+\lambda h(x)f(u)=0, & & \text{in}\ B,\\ &u=0, & & \text{...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7202 |
| _version_ | 1797830536940486656 |
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| author | Tianlan Chen Ruyun Ma |
| author_facet | Tianlan Chen Ruyun Ma |
| author_sort | Tianlan Chen |
| collection | DOAJ |
| description | This paper is concerned with the global behavior of components of positive radial solutions for the quasilinear elliptic problem with indefinite weight
\begin{equation*}
\begin{aligned}
&\text{div}(\varphi_p(\nabla u))+\lambda h(x)f(u)=0, & & \text{in}\ B,\\
&u=0, & & \text{on}\ \partial B,
\end{aligned}
\end{equation*}
where $\varphi_p(s)=|s|^{p-2}s$, $B$ is the unit open ball of $\mathbb{R}^N$ with $N\geq1$, $1<p<\infty$, $\lambda>0$ is a parameter, $f\in C([0, \infty), [0, \infty))$ and $h\in C(\bar{B})$ is a sign-changing function. We manage to determine the intervals of $\lambda$ in which the above problem has one, two or three positive radial solutions by using the directions of a bifurcation. |
| first_indexed | 2024-04-09T13:37:41Z |
| format | Article |
| id | doaj.art-cc65e95e5cbc4e2fb75e723adf7c7a70 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:41Z |
| publishDate | 2019-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-cc65e95e5cbc4e2fb75e723adf7c7a702023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-03-0120191911410.14232/ejqtde.2019.1.197202Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weightTianlan Chen0Ruyun Ma1Department of Mathematics, Northwest Normal University, Lanzhou, P.R. ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou, P.R. ChinaThis paper is concerned with the global behavior of components of positive radial solutions for the quasilinear elliptic problem with indefinite weight \begin{equation*} \begin{aligned} &\text{div}(\varphi_p(\nabla u))+\lambda h(x)f(u)=0, & & \text{in}\ B,\\ &u=0, & & \text{on}\ \partial B, \end{aligned} \end{equation*} where $\varphi_p(s)=|s|^{p-2}s$, $B$ is the unit open ball of $\mathbb{R}^N$ with $N\geq1$, $1<p<\infty$, $\lambda>0$ is a parameter, $f\in C([0, \infty), [0, \infty))$ and $h\in C(\bar{B})$ is a sign-changing function. We manage to determine the intervals of $\lambda$ in which the above problem has one, two or three positive radial solutions by using the directions of a bifurcation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7202positive solutions$p$-laplacianindefinite weightbifurcation |
| spellingShingle | Tianlan Chen Ruyun Ma Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight Electronic Journal of Qualitative Theory of Differential Equations positive solutions $p$-laplacian indefinite weight bifurcation |
| title | Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight |
| title_full | Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight |
| title_fullStr | Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight |
| title_full_unstemmed | Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight |
| title_short | Three positive solutions of $N$-dimensional $p$-Laplacian with indefinite weight |
| title_sort | three positive solutions of n dimensional p laplacian with indefinite weight |
| topic | positive solutions $p$-laplacian indefinite weight bifurcation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7202 |
| work_keys_str_mv | AT tianlanchen threepositivesolutionsofndimensionalplaplacianwithindefiniteweight AT ruyunma threepositivesolutionsofndimensionalplaplacianwithindefiniteweight |