Isabella Ianni

On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials

Abstract We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

SOLUTIONS OF THE SCHRÖDINGER–POISSON PROBLEM CONCENTRATING ON SPHERES, PART I: NECESSARY CONDITIONS

In this paper we study a coupled nonlinear Schrodinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrodinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems

We consider the semilinear Lane-Emden problem in a smooth bounded domain of the plane. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions as the exponent p of the nonlinearity goes to infinity. Among other results we show, under some symmetry assumptions on the domain, that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p goes to infinity, and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville problem in the plane.

Exact Morse index computation for nodal radial solutions of Lane–Emden problems

We consider the semilinear Lane–Emden problem where B is the unit ball of

Asymptotic profile of positive solutions of Lane–Emden problems in dimension two

\mathbb {R}^N

Non-radial sign-changing solutions for the Schrödinger–Poisson problem in the semiclassical limit

RN,

Blow up of solutions of semilinear heat equations in non radial domains of

N\ge 2