8 papers · 1 filter
Some remarks about the Morse index for convex Hamiltonians systems
Anna Lisa Amadori
We investigate the (linearized) Morse index of solutions to Hamiltonan systems, with a focus on convex Hamiltonians functions and sign-changing radial solutions. For strongly coupl…
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}…
Global bifurcation for the Hénon problem
Anna Lisa Amadori
We prove the existence of nonradial solutions for the Hénon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent . For sign-changing s…
On the asymptotically linear Hénon problem
Anna Lisa Amadori
In this paper we consider the Hénon problem in the ball with Dirichlet boundary conditions. We study the asymptotic profile of radial solutions and then deduce the exact computatio…
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's, Part II
Anna Lisa Amadori, Francesca Gladiali
By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in a previous paper, we give a lower bound for the…
The Hénon problem with large exponent in the disc
Anna Lisa Amadori, Francesca Gladiali
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 solut…