INFINITELY MANY POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS

被引：1
|
作者：
Chen, Hong-ge [1 ]
Zhang, J. I. A. O. J. I. A. O. [1 ,2 ]
Zhao, J. I. E. [3 ]
机构：
[1] Chinese Acad Sci, Innovat Acad Precis Measurement Sci & Technol, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China
[2] Univ Chinese Acad Sci, Beijing 100049, Peoples R China
[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年
基金：
中国博士后科学基金;
关键词：
Semilinear elliptic equations; positive solutions; Lyapunov-Schmidt reduction method; SCALAR FIELD-EQUATIONS; PARTICLE-LIKE SOLUTIONS; CRITICAL-POINTS; SCHRODINGER-EQUATIONS; EXISTENCE; MULTIPLICITY; FUNCTIONALS; UNIQUENESS; STABILITY; SYMMETRY;
D O I：
10.3934/dcds.2022130
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For N > 3 and 1 < p < N+2 N-2 , we consider the following semilinear elliptic equation J.-delta u = V (|x|)(|u - 1|p - 1) in RN, (1) u > 0 in RN, u E H1(RN), where V (r) is a positive bounded function satisfying ) a1a2( 1 V (r) = 1 + + r alpha r alpha+1 + O as r-+ +oo. r alpha+1+theta Here a1, theta > 0, a2 E R and alpha > 2(min {1, (p - 1)})-1 are some constants. By the finite dimensional Lyapunov-Schmidt reduction method, we show that (1) has infinitely many non-radial positive solutions.
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页码：5909 / 5935
页数：27
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