Multiple positive solutions for Schrödinger-Poisson system with singularity on the Heisenberg group

被引：0
|
作者：
Tian G. [1 ]
An Y. [1 ]
Suo H. [2 ]
机构：
[1] School of Sciences, Guizhou University of Engineering Science, Bijie
[2] School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang
来源：
Journal of Inequalities and Applications | / 2024卷 / 1期
关键词：
35A15; 35R03; Heisenberg group; Positive solutions; Schrödinger-Poisson system; Singularity;
D O I：
10.1186/s13660-024-03096-3
中图分类号：
学科分类号：
摘要：
In this work, we study the following Schrödinger-Poisson system (Formula presented.) where (Formula presented.) is the Kohn-Laplacian on the first Heisenberg group (Formula presented.), and (Formula presented.) is a smooth bounded domain, (Formula presented.), (Formula presented.), and (Formula presented.) are some real parameters. For the above system, we prove the existence and uniqueness of positive solution for (Formula presented.) and each (Formula presented.). Multiple solutions of the system are also considered for (Formula presented.) and (Formula presented.) small enough using the critical point theory for nonsmooth functional. © The Author(s) 2024.
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