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

doi:10.1016/S0252-9602(13)60066-1

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1099-1112.doi: 10.1016/S0252-9602(13)60066-1

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

孙小妹

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
College of Science, Huazhong Agricultural University, Wuhan 430070, China

收稿日期:2012-04-19 修回日期:2012-06-04 出版日期:2013-07-20 发布日期:2013-07-20
基金资助:
Supported by the National Science Foundation of China (11071245 and 11101418).

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

SUN Xiao-Mei

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
College of Science, Huazhong Agricultural University, Wuhan 430070, China

Received:2012-04-19 Revised:2012-06-04 Online:2013-07-20 Published:2013-07-20
Supported by:
Supported by the National Science Foundation of China (11071245 and 11101418).

摘要/Abstract

摘要：

In this paper, we deal with the following problem:
{−Δ_pu − λ|y|^−p|u|^p−2u = |y|^−s|u|p*^(s)−2u + |u|^p*−2u in R^N, y ≠ 0,
u ≥ 0,
where u(x) = u(y, z) : R^m × R^N−m −→ R, N ≥ 3, 2 < m < N, 1 < p < m, λ <( (m−p)/p )^pand 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.

关键词: p-Laplace equation, cylindrical potential, critical exponents

Abstract:

Key words: p-Laplace equation, cylindrical potential, critical exponents

中图分类号:

35J20

孙小妹. p-LAPLACE EQUATIONS WITH MULTIPLE CRITICAL EXPONENTS AND SINGULAR CYLINDRICAL POTENTIAL[J]. 数学物理学报(英文版), 2013, 33(4): 1099-1112.

SUN Xiao-Mei. p-LAPLACE EQUATIONS WITH MULTIPLE CRITICAL EXPONENTS AND SINGULAR CYLINDRICAL POTENTIAL[J]. Acta mathematica scientia,Series B, 2013, 33(4): 1099-1112.

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

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

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