含Hardy位势的非线性Schrödinger-Poisson方程正规化解的多重性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 442-453.

含Hardy位势的非线性Schrödinger-Poisson方程正规化解的多重性

杜梦雪,李方卉,王征平*()

武汉理工大学数学科学中心武汉 430070

收稿日期:2021-06-23 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 王征平 E-mail:zpwang@whut.edu.cn
基金资助:
国家自然科学基金(11871386);国家自然科学基金(11931012)

Multiplicity of Normalized Solutions for Nonlinear Schrödinger-Poisson Equation with Hardy Potential

Mengxue Du,Fanghui Li,Zhengping Wang*()

Center of Mathematics, Wuhan University of Technology, Wuhan 430070

Received:2021-06-23 Online:2022-04-26 Published:2022-04-18
Contact: Zhengping Wang E-mail:zpwang@whut.edu.cn
Supported by:
the NSFC(11871386);the NSFC(11931012)

摘要/Abstract

摘要：

该文研究了含Hardy位势的非线性Schrödinger-Poisson方程正规化解的多重性问题. 首先利用喷泉定理的思想定义了一个极小极大值序列, 然后证明这些极小极大值是限制在约束集合上的能量泛函的临界值, 从而得到了方程正规化解的多重性, 推广了相关文献的结果.

关键词: Schrödinger-Poisson方程, Hardy位势, 正规化解, 多重性

Abstract:

In this paper, we concern the multiplicity of normalized solutions for a class of nonlinear Schrödinger-Poisson equation with Hardy potential. By using some ideas of the fountain theorem, we define a sequence of minimax values and prove that these minimax values are critical values of the energy functional limited to a constraint set. Then we get the multiplicity of normalized solutions, which extends some related results in the literature.

Key words: Schrödinger-Poisson equation, Hardy potential, Normalized solution, Multiplicity

中图分类号:

O175.2

杜梦雪, 李方卉, 王征平. 含Hardy位势的非线性Schrödinger-Poisson方程正规化解的多重性[J]. 数学物理学报, 2022, 42(2): 442-453.

Mengxue Du, Fanghui Li, Zhengping Wang. Multiplicity of Normalized Solutions for Nonlinear Schrödinger-Poisson Equation with Hardy Potential[J]. Acta mathematica scientia,Series A, 2022, 42(2): 442-453.

参考文献

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