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 .
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页数：21
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