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Volume 18, Issue 2
Minimal Positive Entire Solution of Semilinear Elliptic Equation

Yingfeng Shang & Miaoxin Yao

J. Part. Diff. Eq., 18 (2005), pp. 141-148.

Published online: 2005-05

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  • Abstract

In this paper, the singular semilinear elliptic equation Δu + q(x)u^α + p(x)u^{-β} - h(x)u^{-ϒ} = 0, x ∈ R^N, N ≥ 3, is studied via the super and sub-solution method, where Δ is the Laplacian operator, α ∈ [0, 1), β > 0, and ϒ ≥ 1 are constants. Under a set of suitable assumptions on functions q(x), p(x) and h(x), it is proved that there exists for the equation one and only one minimal positive entire solution.

  • Keywords

Super and sub-solution method minimal positive solution singular semilinear elliptic equation

  • AMS Subject Headings

35J25 35J60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-18-141, author = {Yingfeng Shang and Miaoxin Yao }, title = {Minimal Positive Entire Solution of Semilinear Elliptic Equation}, journal = {Journal of Partial Differential Equations}, year = {2005}, volume = {18}, number = {2}, pages = {141--148}, abstract = {

In this paper, the singular semilinear elliptic equation Δu + q(x)u^α + p(x)u^{-β} - h(x)u^{-ϒ} = 0, x ∈ R^N, N ≥ 3, is studied via the super and sub-solution method, where Δ is the Laplacian operator, α ∈ [0, 1), β > 0, and ϒ ≥ 1 are constants. Under a set of suitable assumptions on functions q(x), p(x) and h(x), it is proved that there exists for the equation one and only one minimal positive entire solution.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5350.html} }
TY - JOUR T1 - Minimal Positive Entire Solution of Semilinear Elliptic Equation AU - Yingfeng Shang & Miaoxin Yao JO - Journal of Partial Differential Equations VL - 2 SP - 141 EP - 148 PY - 2005 DA - 2005/05 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5350.html KW - Super and sub-solution method KW - minimal positive solution KW - singular semilinear elliptic equation AB -

In this paper, the singular semilinear elliptic equation Δu + q(x)u^α + p(x)u^{-β} - h(x)u^{-ϒ} = 0, x ∈ R^N, N ≥ 3, is studied via the super and sub-solution method, where Δ is the Laplacian operator, α ∈ [0, 1), β > 0, and ϒ ≥ 1 are constants. Under a set of suitable assumptions on functions q(x), p(x) and h(x), it is proved that there exists for the equation one and only one minimal positive entire solution.

Yingfeng Shang and Miaoxin Yao . (2005). Minimal Positive Entire Solution of Semilinear Elliptic Equation. Journal of Partial Differential Equations. 18 (2). 141-148. doi:
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