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一类Schr?dinger-Maxwell系统的多解
Multiple Solutions of a Class of Schr?dinger-Maxwell System

DOI: 10.12677/AAM.2022.117445, PP. 4188-4197

Keywords: Schr?dinger-Maxwell系统,Ekeland变分原理,山路定理,多重正解
Schr?dinger-Maxwell System
, Ekeland’s Variational Principle, Mountain Pass Theorem, Multiple Positive Solution

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Abstract:

本文主要研究一类Schr?dinger-Maxwell系统,在一定条件下利用临界点理论中的Ekeland变分原理和山路定理证得该系统存在两个正解,并且其中一个解是正能量解,另一个解是负能量解。
This paper mainly studies a class of Schr?dinger-Maxwell system. Under certain conditions, using the Ekeland’s variational principle and Mountain Pass theorem, it is proved that the system has two positive solutions, one of which is a positive energy solution and the other is a negative energy solu-tion.

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