| Contents |
| We consider the problem
\begin{align*}
-\Delta u &= \lambda u e^{u^p},\quad u>0,\quad\mbox{in}\quad
\Omega,\\
&u= 0\quad \mbox{on}\quad \partial \Omega,
\end{align*}
where $\Omega\subset \mathbb{R}^2$ and $p>2$. Let $\lambda_1$ be
the first eigenvalue of the Laplacian. For each $\lambda \in
(0,\lambda_1)$, we prove the existence of solutions for $p$
sufficiently close to $2$. In the case of $\Omega$ a ball, we
also describe numerically the bifurcation diagram $(\lambda,u)$
for $p>2$. |
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