Sign-changing bubble tower solutions for a supercritical elliptic problem with the Henon term

被引：6

作者：

Chen, Wenjing ^{[1
]}

Deng, Shengbing ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

NONLINEARITY | 2017年 / 30卷 / 12期

基金：

中国博士后科学基金; 美国国家科学基金会;

关键词：

supercritical elliptic equation; Henon term; sign-changing bubble tower solutions; Lyapunov-Schmidt procedure; CRITICAL SOBOLEV EXPONENT; BREZIS-NIRENBERG PROBLEM; POSITIVE SOLUTIONS; DIRICHLET PROBLEM; RADIAL SOLUTIONS; CRITICAL GROWTH; EQUATION; UNIQUENESS; DOMAINS;

D O I：

10.1088/1361-6544/aa870f

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the following elliptic problem with the Henon term {-Delta u = vertical bar x|vertical bar(alpha)vertical bar u vertical bar(p alpha-1-epsilon) u, in Omega, u = 0, on partial derivative Omega where Omega is a bounded smooth domain in R-N containing the origin, N >= 3, and epsilon > 0 small, p(alpha) = N+2+2 alpha/N-2, where alpha > 0 is not an even integer. As epsilon goes to zero, we construct a sign-changing solution with the shape of a tower of bubbles with alternate signs, centered at the origin.

引用

页码：4344 / 4368

页数：25

共 22 条

[1]

Badiale M, 2004, ADV NONLINEAR STUD, V4, P453

[2] Super-critical boundary bubbling in a semilinear Neumann problem [J].

del Pino, M ;

Musso, M ;

Pistoia, A .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2005, 22 (01) :45-82

[3] The Brezis-Nirenberg problem near criticality in dimension 3 [J].

del Pino, M ;

Dolbeault, J ;

Musso, M .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (12) :1405-1456

[4] Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem [J].

Del Pino, M ;

Dolbeault, J ;

Musso, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) :280-306

[5] Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains [J].

Ge, Yuxin ;

Musso, Monica ;

Pistoia, Angela .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (08) :1419-1457

[6] GLOBAL AND LOCAL BEHAVIOR OF POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS [J].

GIDAS, B ;

SPRUCK, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1981, 34 (04) :525-598

[7]

Gladiali F, 2015, DIFFER INTEGRAL EQU, V28, P733

[8] Nonradial solutions for the Henon equation in RN [J].

Gladiali, Francesca ;

Grossi, Massimo ;

Neves, Sergio L. N. .

ADVANCES IN MATHEMATICS, 2013, 249 :1-36

[9] Supercritical elliptic problem with nonautonomous nonlinearities [J].

Gladiali, Francesca ;

Grossi, Massimo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (09) :2616-2645

[10] SOLUTIONS WITH LARGE NUMBER OF PEAKS FOR THE SUPERCRITICAL HENON EQUATION [J].

Liu, Zhongyuan ;

Peng, Shuangjie .

PACIFIC JOURNAL OF MATHEMATICS, 2016, 280 (01) :115-139

← 1 2 3 →