The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity
| dc.creator | del Pino, Manuel | |
| dc.creator | Muñoz, Claudio | |
| dc.date | 2006-08-07 | |
| dc.date.accessioned | 2026-07-07T07:21:28Z | |
| dc.date.available | 2026-07-07T07:21:28Z | |
| dc.description | We 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 $s\to +\infty$. | |
| dc.description | 24 pages, to appear in J. Diff. Eqns | |
| dc.identifier | https://arxiv.org/abs/math/0608168 | |
| dc.identifier | http://arxiv.org/abs/math/0608168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115311 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.title | The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity | |
| dc.type | text |