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Volume 15, Issue 1
Semilinear Elliptic Equations with Singularity on the Boundary

Youdong Zeng & Zuchi Chen

J. Part. Diff. Eq., 15 (2002), pp. 28-34.

Published online: 2002-02

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  • Abstract
In this paper, we consider the existence and nonexistence of positive solutions to semilinear elliptic equation -Δu = K(x)(1-|x|)^{-λ_u^q} in the unit ball B with 0-Dirichlet boundary condition. Our main tools are based on the interior estimates of the Schauder type, the Schauder fixed point theorem and the pointwise estimates for Green functions.
  • Keywords

Singularity semilinear equation positive solution

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@Article{JPDE-15-28, author = {}, title = {Semilinear Elliptic Equations with Singularity on the Boundary}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {1}, pages = {28--34}, abstract = { In this paper, we consider the existence and nonexistence of positive solutions to semilinear elliptic equation -Δu = K(x)(1-|x|)^{-λ_u^q} in the unit ball B with 0-Dirichlet boundary condition. Our main tools are based on the interior estimates of the Schauder type, the Schauder fixed point theorem and the pointwise estimates for Green functions.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5438.html} }
TY - JOUR T1 - Semilinear Elliptic Equations with Singularity on the Boundary JO - Journal of Partial Differential Equations VL - 1 SP - 28 EP - 34 PY - 2002 DA - 2002/02 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5438.html KW - Singularity KW - semilinear equation KW - positive solution AB - In this paper, we consider the existence and nonexistence of positive solutions to semilinear elliptic equation -Δu = K(x)(1-|x|)^{-λ_u^q} in the unit ball B with 0-Dirichlet boundary condition. Our main tools are based on the interior estimates of the Schauder type, the Schauder fixed point theorem and the pointwise estimates for Green functions.
Youdong Zeng & Zuchi Chen . (2019). Semilinear Elliptic Equations with Singularity on the Boundary. Journal of Partial Differential Equations. 15 (1). 28-34. doi:
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