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

被引：3

作者：

Sun, Xiaomei ^{[1
,2
]}

机构：

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

[2] Huazhong Agr Univ, Coll Sci, Wuhan 430070, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 04期

基金：

美国国家科学基金会;

关键词：

p-Laplace equation; cylindrical potential; critical exponents; LINEAR ELLIPTIC-EQUATIONS; GLOBAL COMPACTNESS RESULT; POSITIVE SOLUTIONS; EXISTENCE;

D O I：

10.1016/S0252-9602(13)60066-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we deal with the following problem: {-Delta(p)u - lambda vertical bar y vertical bar(-p)vertical bar u vertical bar(p-2)u = vertical bar y vertical bar(-s)vertical bar u vertical bar(p)*((s)-2)u+ vertical bar u vertical bar(p)*(-2)u in R-n, y not equal 0, u >= 0, where u(x) = u(y, z) :R-m x RN-m -> R, N >= 3, 2 < m < N, 1 < p < m, lambda < (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 < lambda < (m - p/p)(p) and the existence of a cylindrical weak solution when lambda < 0.

引用

页码：1099 / 1112

页数：14

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