Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction
This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition: $ \begin{equation*} \left\{\begin{matrix} -\Delta u+V_{1}(x)u-\Delta (u^{2})u = h(u,v),\ x\in \mathbb{R}^{N},\\ -\Delta v+V_{2}(x)v-\Delta (v^{2})v = g(u,v),\ x\in \mathbb{R}^{N},\\ \end{...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023106?viewType=HTML |
| _version_ | 1827953839951577088 |
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| author | Yixuan Wang Xianjiu Huang |
| author_facet | Yixuan Wang Xianjiu Huang |
| author_sort | Yixuan Wang |
| collection | DOAJ |
| description | This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition:
$ \begin{equation*} \left\{\begin{matrix} -\Delta u+V_{1}(x)u-\Delta (u^{2})u = h(u,v),\ x\in \mathbb{R}^{N},\\ -\Delta v+V_{2}(x)v-\Delta (v^{2})v = g(u,v),\ x\in \mathbb{R}^{N},\\ \end{matrix}\right. \end{equation*} $
where $ N \geq3 $, $ V_{1}(x) $, $ V_{2}(x) $ are variable potentials and $ h $, $ g $ satisfy some conditions. By establishing a suitable Nehari-Pohožaev type constraint set and considering related minimization problem, we prove the existence of ground states. |
| first_indexed | 2024-04-09T14:19:50Z |
| format | Article |
| id | doaj.art-a505feef6fb34405974a18acedcd6b0d |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-09T14:19:50Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-a505feef6fb34405974a18acedcd6b0d2023-05-05T01:28:51ZengAIMS PressElectronic Research Archive2688-15942023-02-013142071209410.3934/era.2023106Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reactionYixuan Wang0Xianjiu Huang1School of Mathematics and Computer Sciences, Nanchang University, Nanchang, Jiangxi 330031, ChinaSchool of Mathematics and Computer Sciences, Nanchang University, Nanchang, Jiangxi 330031, ChinaThis article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition: $ \begin{equation*} \left\{\begin{matrix} -\Delta u+V_{1}(x)u-\Delta (u^{2})u = h(u,v),\ x\in \mathbb{R}^{N},\\ -\Delta v+V_{2}(x)v-\Delta (v^{2})v = g(u,v),\ x\in \mathbb{R}^{N},\\ \end{matrix}\right. \end{equation*} $ where $ N \geq3 $, $ V_{1}(x) $, $ V_{2}(x) $ are variable potentials and $ h $, $ g $ satisfy some conditions. By establishing a suitable Nehari-Pohožaev type constraint set and considering related minimization problem, we prove the existence of ground states. https://www.aimspress.com/article/doi/10.3934/era.2023106?viewType=HTMLquasilinear schrödinger systemsground state solutionspohožaev manifold |
| spellingShingle | Yixuan Wang Xianjiu Huang Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction Electronic Research Archive quasilinear schrödinger systems ground state solutions pohožaev manifold |
| title | Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction |
| title_full | Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction |
| title_fullStr | Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction |
| title_full_unstemmed | Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction |
| title_short | Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction |
| title_sort | ground states of nehari pohozaev type for a quasilinear schrodinger system with superlinear reaction |
| topic | quasilinear schrödinger systems ground state solutions pohožaev manifold |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023106?viewType=HTML |
| work_keys_str_mv | AT yixuanwang groundstatesofneharipohozaevtypeforaquasilinearschrodingersystemwithsuperlinearreaction AT xianjiuhuang groundstatesofneharipohozaevtypeforaquasilinearschrodingersystemwithsuperlinearreaction |