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.

引用

页码：5909 / 5935

页数：27

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