4 papers · 1 filter
Stability and asymptotic behaviour of one-dimensional solutions in cylinders
Francesca De Marchis, Lisa Mazzuoli, Filomena Pacella
We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with r…
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…
Asymptotic analysis for the Lane-Emden problem in dimension two
Francesca De Marchis, Isabella Ianni, Filomena Pacella
We consider the Lane-Emden Dirichlet problem \begin{equation}\tag{1} \left\{\begin{array}{lr}-Δu= |u|^{p-1}u\qquad \mbox{ in }Ωu=0\qquad\qquad\qquad\mbox{ on }\partial Ω\end{array}…