29 citations · 144 across the 45 of their papers we have counts for
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Morse Index and Symmetry for Elliptic Problems with Nonlinear Mixed Boundary Conditions
Lucio Damascelli, Filomena Pacella
Under a Morse index condition we prove symmetry results for solutions of a nonlinear mixed boundary condition elliptic problem. As an intermediate step we relate the Morse index of…
Existence results for fully nonlinear equations in radial domains
Giulio Galise, Fabiana Leoni, Filomena Pacella
We consider the fully nonlinear problem \begin{equation*} \begin{cases} -F(x,D^2u)=|u|^{p-1}u & \text{in }\\ u=0 & \text{on } \end{cases} \end{equation*} where is…
Asymptotic profile of positive solutions of Lane-Emden problems in dimension two
Francesca De Marchis, Isabella Ianni, Filomena Pacella
We consider families of solutions to the problem \begin{equation}\label{problemAbstract} \left\{\begin{array}{lr}-Δu= u^p & \mbox{ in }Ω\\ u>0 & \mbox{ in }Ω\\ u=0 & \mbox{ o…
A Morse index formula for radial solutions of Lane-Emden problems
Francesca De Marchis, Isabella Ianni, Filomena Pacella
We consider the semilinear Lane-Emden problem: \begin{equation}\label{problemAbstract}\left\{\begin{array}{lr}-Δu= |u|^{p-1}u\qquad \mbox{ in }B u=0\qquad\qquad\qquad\mbox{ on }\pa…
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}…
A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain
Filomena Pacella, Michael Plum, Dagmar Rütters
We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden's equation on an unbounded -shaped domain, subject to Di…