NODAL SOLUTIONS FOR A SUPERCRITICAL PROBLEM WITH VARIABLE EXPONENT AND LOGARITHMIC NONLINEARITY

被引：1
|
作者：
Deng, Yinbin [1 ,2 ]
Zhang, Xinyue [1 ,2 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2023年 / 43卷 / 12期
关键词：
Sign-changing solutions; variable exponent; supercritical problem; SIGN-CHANGING SOLUTIONS; SCHRODINGER-EQUATIONS; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; EXISTENCE; CHARACTER;
D O I：
10.3934/dcds.2023093
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the existence of sign-changing solutions for the following supercritical problem with variable exponent and logarithmic nonlinearity {-Delta u = vertical bar u vertical bar(2* -2)u( ln(tau + vertical bar u vertical bar))(vertical bar x vertical bar beta) in B-1, u = 0 on partial derivative B-1, where B-1 is the unit ball in R-N, N = 3, 2* = 2N/(N - 2) is the critical Sobolev exponent, and tau >= 1, beta > 0 are constants. For any k is an element of N, if tau >= 1 and 0 < beta < (N - 2)/2, we show that there exist one pair of solutions which change sign exactly k times by variational methods.
引用
收藏
页码：4429 / 4453
页数：25
相关论文
共 50 条
12345