A uniqueness result for some singular semilinear elliptic equations

Annamaria Canino; Berardino Sciunzi

A uniqueness result for some singular semilinear elliptic equations

Analysis of PDEs 2014-07-23 v1

Authors: Annamaria Canino , Berardino Sciunzi

Abstract

Given $\Omega$ a bounded open subset of $\mathbb{R}^N$ , we consider nonnegative solutions to the singular semilinear elliptic equation $-\Delta\,u\,=\,\frac{f}{u^{\beta}}$ in $H^1_{loc}(\Omega)$ , under zero Dirichlet boundary conditions. For $\beta>0$ and $f\in L^1(\Omega)$ , we prove that the solution is unique.

Keywords

positive solutions of elliptic equations singular solutions of pdes semilinear elliptic equations

Cite

@article{arxiv.1407.5984,
  title  = {A uniqueness result for some singular semilinear elliptic equations},
  author = {Annamaria Canino and Berardino Sciunzi},
  journal= {arXiv preprint arXiv:1407.5984},
  year   = {2014}
}

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