p-LAPLACE EQUATIONS WITH MULTIPLE CRITICAL EXPONENTS AND SINGULAR CYLINDRICAL POTENTIAL

被引：0

作者：

孙小妹 ^{[1
,2
]}

机构：

[1] Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences

[2] College of Science, Huazhong Agricultural University

来源：

Acta Mathematica Scientia | 2013年 / 33卷 / 04期

关键词：

p-Laplace equation; cylindrical potential; critical exponents;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper,we deal with the following problem: {-△pu-λ|y|-p|u|p-2u = |y|-s|u|p*(s)-2u+|u|p*-2u in RN,y = 0,u ≥ 0,where u(x) = u(y,z) : Rm×RN m →R,N≥ 3,2 < m < N,1 < p < m,λ <((m-p)/p)p and 0 < s < p,p*(s) =(p(N-s))/(N-p),p*=pN/(N-p).By variational method,we prove the existence of a nontrivial weak solution when 0 < λ <((m-p)/p)p and the existence of a cylindrical weak solution when λ < 0.

引用

页码：1099 / 1112

页数：14

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