SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATION IN R^n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, 2） 〈 β＋ 1 〈 p＊ = Np/N-p We prove that there exists a critical value A such that the problem has at le...

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Bibliographic Details
Published in:Journal of systems science and complexity 2009-12, Vol.22 (4), p.597-613
Main Authors: Liu, Xiangqing, Guo, Yuxia, Liu, Jiaquan
Format: Article
Language:English
Subjects:
Laplace方程
临界值
拉普拉斯方程
正解的存在性
非奇异
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Summary:In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, 2） 〈 β＋ 1 〈 p＊ = Np/N-p We prove that there exists a critical value A such that the problem has at least two solutions if 0 〈 λ 〈 A; at least one solution if λ= A; and no solutions if λ〉A.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-009-9190-6