NORMALIZED SOLUTIONS FOR CHOQUARD EQUATIONS WITH GENERAL NONLINEARITIES

被引：26

作者：

Yuan, Shuai ^{[1
]}

Chen, Sitong ^{[1
]}

Tang, Xianhua ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2020年 / 28卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Choquard equations; normalized solution; variational method; minimax method; weak solutions; SCHRODINGER-POISSON SYSTEM; GROUND-STATE SOLUTIONS; NEHARI-POHOZAEV TYPE; PRESCRIBED NORM; EXISTENCE;

D O I：

10.3934/era.2020017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the existence of positive solutions with prescribed L-2-norm to the following Choquard equation: -Delta u - lambda u = (I-alpha * F(u)) f(u), x is an element of R-3, where lambda is an element of R, alpha is an element of (0,3) and I-alpha : R-3 -> R- ( ) is the Riesz potential. Under the weaker conditions, by using a minimax procedure and some new analytical techniques, we show that for any c > 0, the above equation possesses at least a couple of weak solution((u) over barc, (lambda) over barc) is an element of S-c x R(- )such that parallel to(u) over barc parallel to(2)(2) = c.

引用

页码：291 / 309

页数：19

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