Calculus of Variations and Geometric Measure Theory

Uniqueness and existence results via Morse index for Lane Emden problems

Francesca De Marchis

created by malchiodi on 23 May 2018

29 may 2018 -- 14:00   [open in google calendar]

Scuola Normale Superiore, Aula Tonelli


We consider the classical Lane Emden equation in bounded domains of the plane with Dirichlet boundary conditions and we present some results concerning the Morse index of solutions to this problem, when the exponent of the nonlinearity is large. Via these Morse index computations and a precise asymptotic analysis we can deduce a uniqueness result for positive solutions in convex domains and also some existence results of non-radial sign-changing solutions in the ball. Based on joint papers with M. Grossi, I. Ianni and F. Pacella.