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Morse index, topological degree and local uniqueness of multi-spikes solutions to the Lane-Emden problem in dimension two
Isabella Ianni, Peng Luo, Shusen Yan
We consider multi-spike positive solutions to the Lane-Emden problem in any bounded smooth planar domain and compute their Morse index, extending to the dimension classical t…
Morse index computation for radial solutions of the {Hé}non problem in the disk
Annalisa Amadori, Francesca De Marchis, Isabella Ianni
We compute the Morse index of any radial solution of the semilinear problem: \begin{equation} \label{problemaAbstract}\tag{P} \left\{ \begin{array}{lr}…
Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two
Massimo Grossi, Isabella Ianni, Peng Luo +1
We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -Δu=u^{p} &{\text{in}~Ω},\\[0.5mm] u>0 &{\text{in}~Ω},\\[0.5mm] u=0 &{\text{on}~\partial Ω}, \end{cases…
Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems
Isabella Ianni, Alberto Saldana
We consider the equation for any , either in or in the unit ball of centered at the origin with Dirichlet or Neumann…
Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains
Francesca De Marchis, Massimo Grossi, Isabella Ianni +1
We compute the Morse index of -spike solutions of the semilinear elliptic problem \begin{equation}\label{abstr} \tag{} \begin{cases} -Δu= u^p & \text{in } \\ u=…
Asymptotic analysis and energy quantization for the Lane-Emden problem in dimension two
Francesca De Marchis, Massimo Grossi, Isabella Ianni +1
We complete the study of the asymptotic behavior, as , of the positive solutions to \[ \left\{\begin{array}{lr}-Δu= u^p & \mbox{in}Ω\\ u=0 &\mbox{on}\partial…