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

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COPYRIGHT: © Global Science Press

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@Article{JPDE-18-141, author = {}, 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 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 & Miaoxin Yao . (2019). Minimal Positive Entire Solution of Semilinear Elliptic Equation. Journal of Partial Differential Equations. 18 (2). 141-148. doi:
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