Communications on Pure and Applied Analysis (CPAA)

On positive solution to a second order elliptic equation with a singular nonlinearity

Pages: 1335 - 1343, Volume 9, Issue 5, September 2010      doi:10.3934/cpaa.2010.9.1335

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Galina V. Grishina - Department of Applied Mathematics, Bauman Moscow State Technical University, 2-aya Baumanskaya, 5, 105005 Moscow, Russian Federation (email)

Abstract: We consider a second order elliptic equation with measurable bounded coefficients

$ (a_{ij}(x)u_{x_i})_{x_j}+p(x)|x|^su^{-\sigma}=0, x\in\Omega \setminus \{ O\}, $

where $\sigma >0$, $s$ is any real number, and $\Omega\subset R^n$, $n\ge 3$ is a bounded domain, which contains the origin $O$.
    The aim of this paper is to establish existence, nonexistence and behavior of positive weak solutions near the isolated singularity $O$.

Keywords:  Elliptic equation, singular point, singular nonlinearity, positive solution, existence, nonexistence.
Mathematics Subject Classification:  Primary: 35J15, 35J61, 35J75; Secondary: 35A01, 35Bxx.

Received: August 2009;      Revised: October 2009;      Available Online: May 2019.