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Existence of positive solutions for a singular p-Laplacian differential equation

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An Erratum to this article was published on 15 November 2009

Abstract

In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation

$$ (\varphi _p (u'))' + \frac{\beta } {r}\varphi _p (u') - \gamma \frac{{|u'|^p }} {u} + g(r) = 0,0 < r < 1, $$

subject to the Dirichlet boundary conditions: u(0) = u(1) = 0, where ϕ p (s) = |s|p−2 s,p > 2, β > 0, γ > \( \tfrac{{p - 1}} {p} \)(β + 1), and g(r) ∈ C 1[0, 1] with g(r) > 0 for all r ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.

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Authors and Affiliations

  1. Department of Mathematics, Shenzhen University, Shenzhen, 518060, P. R. China

    Xia Li

  2. Department of Mathematics, Zhongshan University, Guangzhou, 510275, P. R. China

    Zheng An Yao

  3. Department of Mathematics, Jilin University, Changchun, 130012, P. R. China

    Wen Shu Zhou

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  1. Xia Li
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  2. Zheng An Yao
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  3. Wen Shu Zhou
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Correspondence to Xia Li.

Additional information

Supported by National Natural Science Foundation of China 2004 (NNSFC-10171113 and NNSFC-10471156), Tianyuan Youth Foundation (No. 10626056) and Natural Science Foundation of GuangDong 2004 (NSFGD-4009793)

An erratum to this article is available at http://dx.doi.org/10.1007/s10114-009-6238-4.

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Li, X., Yao, Z.A. & Zhou, W.S. Existence of positive solutions for a singular p-Laplacian differential equation. Acta. Math. Sin.-English Ser. 24, 1331–1344 (2008). https://doi.org/10.1007/s10114-008-6238-9

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  • DOI: https://doi.org/10.1007/s10114-008-6238-9

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