POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS

doi:10.1016/S0252-9602(12)60075-7

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1002-1020.doi: 10.1016/S0252-9602(12)60075-7

POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS

王影^1*|罗党¹|王明新²

1.School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China； 2.Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China

收稿日期:2010-09-26 出版日期:2012-05-20 发布日期:2012-05-20
通讯作者: 王影,feelyeey@163.com E-mail:feelyeey@163.com
基金资助:
This work was supported by the National Natural Science Foundation of China 10771032.

POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS

WANG Ying^1*, LUO Dang¹, WANG Ming-Xin²

1.School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China； 2.Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China

Received:2010-09-26 Online:2012-05-20 Published:2012-05-20
Contact: WANG Ying,feelyeey@163.com E-mail:feelyeey@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China 10771032.

摘要/Abstract

摘要：

By the Mountain Pass Theorem, we study existence and multiplicity of posi-tive solutions of p-laplacian equation of the form −Δ_pu = λf(x, u), the nonlinearity f(x, u) grows as u^σ at infinity with a singular coefficient, where σ∈ (p − 1, p*− 1). To manage the asymptotic behavior of its positive solutions with respect to λ, we establish a new Liouville-type theorem for the p-Laplacian operator.

关键词: p-Laplacian, variational methods, Sobolev-Hardy exponents

Abstract:

Key words: p-Laplacian, variational methods, Sobolev-Hardy exponents

中图分类号:

35J15

王影, 罗党, 王明新. POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS[J]. 数学物理学报(英文版), 2012, 32(3): 1002-1020.

WANG Ying, LUO Dang, WANG Ming-Xin. POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS[J]. Acta mathematica scientia,Series B, 2012, 32(3): 1002-1020.

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POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS

POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS

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