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

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

作　　者：杜梦雪 李方卉[1] 王征平[1] Du Mengxue;Li Fanghui;Wang Zhengping(Center of Mathematics,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学数学科学中心,武汉430070

出　　处：《数学物理学报（A辑）》2022年第2期442-453,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871386,11931012)。

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.In this paper,we concern the multiplicity of normalized solutions for a class of nonlinear Schrodinger-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.

关 键 词：Schrödinger-Poisson方程 HARDY位势 正规化解 多重性 

分 类 号：O175.2[理学—数学]