| 一类Schrödinger-Poisson系统非平凡解的存在性 |
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| 引用本文： | 陈丽珍,冯晓晶,李刚.一类Schrödinger-Poisson系统非平凡解的存在性[J].山东大学学报(理学版),2019,54(10):74-78. |
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| 作者姓名： | 陈丽珍 冯晓晶 李刚 |
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| 作者单位： | 1.山西财经大学应用数学学院, 山西 太原 030006;2.山西大学数学科学学院, 山西 太原 030006;3.扬州大学数学科学学院, 江苏 扬州 225002 |
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| 基金项目： | 国家自然科学基金青年科学基金资助项目(11701346) |
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| 摘 要： | 利用变分方法和临界点理论,研究了一类Schrödinger-Poisson系统,其中泊松项为更一般的形式,通过给非线性项加拟临界增长和AR条件,得到了该系统非平凡解的存在性。补充和推广了以往研究Schrödinger-Poisson系统的相关结果。
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| 关 键 词： | Schrö dinger-Poisson系统 变分方法 山路定理 |
Existence of nontrival solutions for a class of Schrödinger-Poisson systems |
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| CHEN Li-zhen,FENG Xiao-jing,LI Gang.Existence of nontrival solutions for a class of Schrödinger-Poisson systems[J].Journal of Shandong University,2019,54(10):74-78. |
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| Authors: | CHEN Li-zhen FENG Xiao-jing LI Gang |
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| Affiliation: | 1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China;2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China;3. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, Jiangsu, China |
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| Abstract: | We investigate a class of Schrödinger-Poisson systems, by means of variational method and critical point theory. Here, the Poisson term is a more general form. By adding quasi-critical growth and AR conditions to the nonlinear term, we prove the existence of nontrival solution of the system. The result supplement and promote the previous resluts on the Schrödinger-Poisson systems. |
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| Keywords: | Schrö dinger-Poisson system variational method mountain pass theorem |
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