Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system
In this paper, we consider the quasilinear Schrödinger system in $\mathbb R^{N}$ ($N\geq3$): \begin{equation*} \begin{cases} -\Delta u+ A(x)u-\frac{1}{2}\Delta(u^{2})u=\frac{2\alpha }{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+ Bv-\frac{1}{2}\Delta(v^{2})v=\frac{2\beta }{\alpha+\beta}|u|...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2022-11-01
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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=9512 |
| _version_ | 1797830421168259072 |
|---|---|
| author | Jianqing Chen Qian Zhang |
| author_facet | Jianqing Chen Qian Zhang |
| author_sort | Jianqing Chen |
| collection | DOAJ |
| description | In this paper, we consider the quasilinear Schrödinger system in $\mathbb R^{N}$ ($N\geq3$):
\begin{equation*}
\begin{cases}
-\Delta u+ A(x)u-\frac{1}{2}\Delta(u^{2})u=\frac{2\alpha }{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\
-\Delta v+ Bv-\frac{1}{2}\Delta(v^{2})v=\frac{2\beta }{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,
\end{cases}
\end{equation*}
where $\alpha,\beta>1$, $2<\alpha+\beta<\frac{4N}{N-2}$, $B>0$ is a constant. By using a constrained minimization on Nehari–Pohožaev set, for any given integer $s\geq2$, we construct a non-radially symmetrical nodal solution with its $2s$ nodal domains. |
| first_indexed | 2024-04-09T13:35:47Z |
| format | Article |
| id | doaj.art-1b8e0e82c52843178e68750d75d3eb2f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:35:47Z |
| publishDate | 2022-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1b8e0e82c52843178e68750d75d3eb2f2023-05-09T07:53:12ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752022-11-0120225711410.14232/ejqtde.2022.1.579512Multiple nonsymmetric nodal solutions for quasilinear Schrödinger systemJianqing Chen0Qian Zhang1College of Mathematics and Computer Science, Fujian Normal University, Qishan Campus, Fuzhou, P.R. ChinaDepartment of Mathematical Sciences, Tsinghua University, Beijing, P.R. ChinaIn this paper, we consider the quasilinear Schrödinger system in $\mathbb R^{N}$ ($N\geq3$): \begin{equation*} \begin{cases} -\Delta u+ A(x)u-\frac{1}{2}\Delta(u^{2})u=\frac{2\alpha }{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+ Bv-\frac{1}{2}\Delta(v^{2})v=\frac{2\beta }{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v, \end{cases} \end{equation*} where $\alpha,\beta>1$, $2<\alpha+\beta<\frac{4N}{N-2}$, $B>0$ is a constant. By using a constrained minimization on Nehari–Pohožaev set, for any given integer $s\geq2$, we construct a non-radially symmetrical nodal solution with its $2s$ nodal domains.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9512quasilinear schrödinger systemnehari–pohožaev setnon-radially symmetrical nodal solutions. |
| spellingShingle | Jianqing Chen Qian Zhang Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system Electronic Journal of Qualitative Theory of Differential Equations quasilinear schrödinger system nehari–pohožaev set non-radially symmetrical nodal solutions. |
| title | Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system |
| title_full | Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system |
| title_fullStr | Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system |
| title_full_unstemmed | Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system |
| title_short | Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system |
| title_sort | multiple nonsymmetric nodal solutions for quasilinear schrodinger system |
| topic | quasilinear schrödinger system nehari–pohožaev set non-radially symmetrical nodal solutions. |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9512 |
| work_keys_str_mv | AT jianqingchen multiplenonsymmetricnodalsolutionsforquasilinearschrodingersystem AT qianzhang multiplenonsymmetricnodalsolutionsforquasilinearschrodingersystem |