Sesión Ecuaciones Diferenciales y AplicacionesA mixed local and nonlocal Hénon problem in \(\mathbb{R}^n\)
Pablo Ochoa
Facultad de Ingeniería, UNCUYO-CONICET, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
The classical Hénon problem consists of finding a solution to \[\label{intro.henon} -\Delta u = |x|^\alpha u^{q-1} \text{ in } B\subset \mathbb{R}^N, \qquad u>0,\] with Dirichlet boundary conditions, where \(B\) denotes the unit ball in \(\mathbb{R}^N\). The motivation in Hénon’s original paper was a model of stationary solutions of the nonlinear Poisson equation describing cluster density under gravitational interaction with inhomogeneous distribution. In this direction, it was established later that the weight \(|x|^\alpha\) allows for a wider admissible range of exponents for which solutions exist (including the critical Sobolev exponent). In this talk, we will discuss a generalization of the Hénon problem that involves an operator with local and nonlocal contributions in the whole space. This is a joint work with Ariel Salort (Universidad San Pablo-CEU, Madrid).