| Contents |
| Let $\Omega$ be a domain in $\mathbb{R}^N, N \geq 2$, $\lambda>0$ a bifurcation parameter and $f: \mathbb{R} \to \mathbb{R}$ a ``real analytic" type map such that $f(t)$ has superlinear growth as $t \to \infty$.
We consider semilinear elliptic PDEs with the presence of a strong singular term as below:
\begin{eqnarray*}
( P_\lambda)\qquad \left\{\begin{array}
{ll}
& - \Delta u
= \lambda(u^{-\delta}+ f(u))
\quad \mbox{ in }\,\Omega ,\\
&u> 0\quad \mbox{ in }\,\Omega, \;\;u\vert_{\partial\Omega} = 0.
\end{array}\right.
\end{eqnarray*}
Here the singular exponent $\delta$ is allowed to be any positive number.
We are interested in this work to analyse the problem $(P_\lambda)$ using the framework of analytic bifurcation theory as developed in the works of Buffoni, Dancer and Toland. We obtain an analytic global unbounded path of solutions to $(P_\lambda)$ for any $\delta>0$ using this framework. |
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