| Abstract: |
| We first review the main features of the paradigmatic class of superlinear boundary value problems
\begin{equation*}
-u``= \lambda u + a(x) u^{p}, \qquad u(0)=u(L)=0,
\end{equation*}
where $p > 1$, $\lambda \in\mathbb{R}$ is regarded as a parameter, and $a(x)$ is a weight function.
Next, we present a solution to a conjecture by R.~G\`{o}mez-Re\~{n}asco and J.~L\`{o}pez-G\`{o}mez (JDE, 2000) concerning the multiplicity of positive solutions.
This is a joint work in collaboration with Juli\`{a}n L\`{o}pez-G\`{o}mez (Universidad Complutense de Madrid) and Juan Carlos Sampedro (Universidad de Cantabria). |
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