On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential
Manuela Yuste Chaves, Jesús García-Azorero · Journal of the European Mathematical Society · 2006
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 $0\<q<\frac{N+2}{N-2}$, $q eq 1$, $\lambda \ge 0$ and $\Omega$ is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.