一类Schrödinger-Poisson系统非平凡解的存在性

doi:10.6040/j.issn.1671-9352.0.2018.638

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (10): 74-78.doi: 10.6040/j.issn.1671-9352.0.2018.638

• • 上一篇

一类Schrödinger-Poisson系统非平凡解的存在性

陈丽珍¹,冯晓晶²,李刚³

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

发布日期:2019-10-12
作者简介:陈丽珍(1982— ),女,博士,副教授,研究方向为非线性泛函分析及应用. E-mail:chenlz409@126.com
基金资助:
国家自然科学基金青年科学基金资助项目(11701346)

Existence of nontrival solutions for a class of Schrödinger-Poisson systems

CHEN Li-zhen¹, FENG Xiao-jing², LI Gang³

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

Published:2019-10-12

摘要/Abstract

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。

关键词: Schrö, dinger-Poisson系统, 变分方法, 山路定理

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.

Key words: Schrö, dinger-Poisson system, variational method, mountain pass theorem

中图分类号:

O176.3

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.

CHEN Li-zhen, FENG Xiao-jing, LI Gang. Existence of nontrival solutions for a class of Schrödinger-Poisson systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 74-78.

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一类Schrödinger-Poisson系统非平凡解的存在性

Existence of nontrival solutions for a class of Schrödinger-Poisson systems

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