Por Ederson Moreira dos Santos (Universidade de São Paulo - São Carlos - Brazil).

Abstract: The Hénon equation, used for modeling some phenomena in astrophysics, is an excellent prototype for the investigation/introduction of some important problems on the qualitative analysis of solutions of elliptic partial differential equations. In this lecture I will address the following themes: The critical exponent for the H ́enon equation; The symmetry of the least energy solutions; The symmetry of the least energy nodal solutions; The Morse index of radial nodal solutions; Some concentration phenomena.