On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential

  • Manuela Chaves

    Universidad Autónoma de Madrid, Spain
  • Jesús García-Azorero

    Universidad Autónoma de Madrid, Spain

Abstract

We will present some results concerning the problem

\[ \label{eq:sl} \left\{ \begin{array}{ll} & -\D u = \lambda \dfrac {u}{|x|^2}+u^q \, , \, \, u > 0 \hbox{ in }\O,\\ & u|_{\p \O}=0, \end{array} \right. \]

where , , and is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.

Cite this article

Manuela Chaves, Jesús García-Azorero, On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 229–242

DOI 10.4171/JEMS/49