Sign-changing solutions for supercritical elliptic problems in domains with small holes

被引：15

作者：

Dancer, E. N. ^{[1
]}

Wei, Juncheng

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

MANUSCRIPTA MATHEMATICA | 2007年 / 123卷 / 04期

关键词：

Primary; 35B40; 35B45; Secondary; 35J40; 92C40; BOUNDARY-VALUE-PROBLEMS; ROTATIONAL SYMMETRY; POSITIVE SOLUTIONS; RADIAL SOLUTIONS; NODAL SOLUTIONS; EQUATIONS; EXISTENCE; BALL;

D O I：

10.1007/s00229-007-0110-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let D be a bounded, smooth domain in R-N, N >= 3, P is an element of D. We consider the boundary value problem in Omega = D\B delta(P), [GRAPHICS] with p supercritical, namely p > N+2/N-2. Given any positive integer m, we find a sequence p(1) < p(2) < p(3) < ..., with lim (k ->+infinity) p(k) = + infinity, such that if p is given, with p not equal p(j) for all j, then for all delta > 0 sufficiently small, this problem has a sign- changing solution which has exactly m + 1 nodal domains.

引用

页码：493 / 511

页数：19

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