. Departamento de Matemática, Universidad Técnica Federico Santa María
In this talk we review some results concerning with the existence and multiplicity of positive solutions for semilinear elliptic problems resembling the following form
$$
\begin{cases}
-\Delta u=\lambda f(u), &\textrm{in }\Omega\\ u=0, &\textrm{on }\partial\Omega,
\end{cases}
$$
where $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$, $N\geq 3$, $f$ is a locally Lipschitz function defined in $[0,+\infty)$, which is nonnegative with a positive zero, and $\lambda$ is a positive parameter. We will also explore how these results can be extended to the fractional operators.