JournalsjemsVol. 8 , No. 2DOI 10.4171/jems/49

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

Abstract

We will present some results concerning the problem

\labeleq:sl{\Du=λux2+uq,u>0 in \O,u\p\O=0,\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 0<q<N+2N20<q<\frac{N+2}{N-2}, q1q\neq 1, λ0\lambda \ge 0 and Ω\Omega is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.