数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 60-79.
收稿日期:
2022-09-20
修回日期:
2023-10-16
出版日期:
2024-02-26
发布日期:
2024-01-10
通讯作者:
徐子怡, E-mail:XuZiyi0822@outlook.com
作者简介:
温瑞江, E-mail:
Wen Ruijiang1(),Liu Fanqin2(
),Xu Ziyi3,*(
)
Received:
2022-09-20
Revised:
2023-10-16
Online:
2024-02-26
Published:
2024-01-10
摘要:
该文考虑次临界 Choquard 方程
{−Δu+(λV(x)+1)u=(∫RN|u(y)|pε|x−y|μdy)|u|pε−2u,x∈RN,u∈H1(RN)(0.1)
多解的存在性, 其中N>3,λ是正实参数,pε=2∗μ−ε,ε>0,0<μ<N,2∗μ=2N−μN−2是 Hardy-Littlewood-Sobolev 不等式意义下的临界指数. 假定Ω:=intV−1(0)是RN中非空带光滑边界的有界区域, 利用 Lusternik-Schnirelman 定理,该文证明了当λ足够大及ε充分小时, 方程(0.1)至少有catΩ(Ω)个正解.
中图分类号:
温瑞江, 刘范琴, 徐子怡. 次临界 Choquard 方程的多解[J]. 数学物理学报, 2024, 44(1): 60-79.
Wen Ruijiang, Liu Fanqin, Xu Ziyi. Multiplicity of Positive Solutions to Subcritical Choquard Equation[J]. Acta mathematica scientia,Series A, 2024, 44(1): 60-79.
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