2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115311We consider the problem of Ambrosetti-Prodi type \begin{equation}\label{0}\quad\begin{cases} Δu + e^u = sϕ_1 + h(x) &\hbox{in} Ω, u=0 & \hbox{on} \partial Ω, \end{cases} \nonumber \end{equation} where $Ω$ is a bounded, smooth domain in $\R^2$, $ϕ_1$ is a positive first eigenfunction of the Laplacian under Dirichlet boundary conditions and $h\in\mathcal{C}^{0,α}(\barΩ)$. We prove that given $k\ge 1$ this problem has at least $k$ solutions for all sufficiently large $s>0$, which answers affirmatively a conjecture by Lazer and McKenna \cite{LM1} for this case. The solutions found exhibit multiple concentration behavior around maxima of $ϕ_1$ as $s\to +\infty$.24 pages, to appear in J. Diff. EqnsAnalysis of PDEsMathematical Physicstext