Non-degeneracy of the bubble solutions for the Henon equation and applications

被引：1

作者：

Guo, Yuxia ^{[1
]}

Hu, Yichen ^{[1
]}

Liu, Ting ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing, Peoples R China

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2023年 / 202卷 / 01期

关键词：

Henon equation; Non-degeneracy; Local Pohozaev identities; Critical Sobolev exponent; New bubble solutions; GROUND-STATE SOLUTIONS; ASYMPTOTIC-BEHAVIOR; PROFILE;

D O I：

10.1007/s10231-022-01231-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following Henon equation with critical growth: {-Delta u = K(vertical bar y vertical bar)u(N+2/N-2), u > 0, in B-1(0) u = 0, on partial derivative B-1(0), where B-1(0) is the unit ball in R-N, K : [0, 1] -> R+ is a bounded function and K ''(1) exists. We prove a non-degeneracy result of the bubble solutions constructed in [24] via the local Pohozaev identities for N >= 5. Then, as applications, by using reduction arguments combined with delicate estimates for the modified Green function and the error, we prove the new existence of infinitely many non-radial solutions, whose energy can be arbitrarily large.

引用

页码：15 / 58

页数：44

共 24 条

[21] Partial symmetry and asymptotic behavior for some elliptic variational problems [J].

Smets, D ;

Willem, M .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2003, 18 (01) :57-75

[22] Non-radial ground states for the Henon equation [J].

Smets, D ;

Willem, M ;

Su, JB .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2002, 4 (03) :467-480

[23]

Swanson C.A., 1992, Appl. Anal., V47, P227, DOI DOI 10.1080/00036819208840142

[24] Infinitely many nonradial solutions for the Henon equation with critical growth [J].

Wei, Juncheng ;

Yan, Shusen .

REVISTA MATEMATICA IBEROAMERICANA, 2013, 29 (03) :997-1020

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