On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's

AL Amadori, F Gladiali - Nonlinear Analysis: Real World Applications, 2020 - Elsevier
We investigate nodal radial solutions to semilinear problems of type− Δ u= f (| x|, u) in Ω, u=
0 on∂ Ω, where Ω is a bounded radially symmetric domain of RN (N≥ 2) and f is a real …

[HTML][HTML] The Hénon problem with large exponent in the disc

AL Amadori, F Gladiali - Journal of Differential Equations, 2020 - Elsevier
In this paper we consider the Hénon problem in the unit disc with Dirichlet boundary
conditions. We study the asymptotic profile of least energy and nodal least energy radial …

On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's: II

AL Amadori, F Gladiali - Nonlinearity, 2020 - iopscience.iop.org
By using a characterization of the Morse index and the degeneracy in terms of a singular
one dimensional eigenvalue problem given in Amadori AL and Gladiali F (2018 arxiv …

Morse index computation for radial solutions of the Hénon problem in the disk

AL Amadori, F De Marchis, I Ianni - Nonlinear Analysis, 2022 - Elsevier
We compute the Morse index m (up) of any radial solution up of the semilinear problem:(P)−
Δ u=| x| α| u| p− 1 u in B u= 0 on∂ B where B is the unit ball of R 2 centered at the origin, α≥ …