Nodal solutions for a zero-mass Chern-Simons-Schrödinger equation

被引：0

作者：

Deng, Yinbin ^{[2
,3
]}

Liu, Chenchen ^{[4
]}

Yang, Xian ^{[1
]}

机构：

[1] Guangxi Univ, Sch Math & Informat Sci, Nanning 530004, Peoples R China

[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[3] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Wuhan 430079, Peoples R China

[4] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2024年 / 13卷 / 01期

基金：

国家重点研发计划;

关键词：

Gauged Schr & ouml; dinger equation; nodal solution; zero mass; variational methods; NONLINEAR SCHRODINGER-EQUATION; STANDING WAVES; NORMALIZED SOLUTIONS; EXISTENCE; MULTIPLICITY;

D O I：

10.1515/anona-2024-0055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study deals with the existence of nodal solutions for the following gauged nonlinear Schr & ouml;dinger equation with zero mass: -Delta u+{(h(u)(2)(divided by x divided by)/(2)(divided by x divided by)+ integral(+infinity)(divided by x divided by)h(u)(s)/(s)u(2)(s)ds}u=divided by u divided by(p-2)u,x is an element of R-2, where p>6 and h(u)(s)=(1)/(2)integral(s)(0)ru(2)(r)dr . By variational methods, we prove that for any integer k >= 0 , the above equation has a nodal solution w(k) which changes sign exactly k times. Moreover, we also prove that w(k) belongs to L-2(R-2) provided p>10 .

引用

页数：21

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