| 陈征艳,张家锋.一类具有陡峭位势临界的分数阶Schrödinger-Poisson系统的基态解[J].井冈山大学自然版,2024,45(6):27-35 |
| 一类具有陡峭位势临界的分数阶Schrödinger-Poisson系统的基态解 |
| GROUND STATE SOLUTIONS FOR A CLASS OF CRITICAL FRACTIONAL SCHRÖDINGER-POISSON SYSTEM WITH STEEP POTENTIAL WELL |
| 投稿时间：2024-06-10 修订日期：2024-07-20 |
| DOI：10.3969/j.issn.1674-8085.2024.06.005 |
| 中文关键词: 基态解 变分方法 临界增长 陡峭位势 分数阶Schrödinger-Poisson系统 |
| 英文关键词: ground state solutions variational methods critical growth steep potential well fractional Schrödinger-Poisson system |
| 基金项目:国家自然科学基金项目(11861021)；贵州省教育厅自然科学研究项目(QJJ2023012,QJJ2023061,QJJ2023062)；贵州民族大学自然科学研究项目(GZMUZK[2022]YB06). |
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| 中文摘要: |
| 研究了一类具有陡峭位势的临界分数阶Schrödinger-Poisson系统。由于能量泛函的最小值大于零，这使得变分法难以运用和实现，为克服这个困难，构造了Pohozaev型等式和Nehari-Pohozaev-Palais-Smale序列。对非线性项f和参数作适当的假设，通过变分方法，得到了基态解的存在性。 |
| 英文摘要: |
| In this paper we study the ground state solutions for a class of critical fractional Schrödinger-Poisson system. Since the minimum value of the energy functional is greater than zero, which can not be easily obtained by variational method, thus, the Pohozaev type identity and the Nehari-Pohozaev-Palais-Smale sequence are constructed to overcome this difficulty. Under suitable assumptions for nonlinear terms f and parameters, by the variational methods, the existence of the ground states solutions is obtained. |
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