A mixed local-nonlocal Hénon problem in ${\mathbb{R}}^N$

Abstract

In this article, we study a Hénon-type equation in ${\mathbb{R}}^N$ driven by a nonlinear operator given by the combination of a local and a nonlocal term. This equation was originally proposed to model spherically symmetric stellar clusters. Here, we prove that, under a suitable relation among the parameters, there exists a threshold separating the existence and non-existence of solutions. Moreover, we establish regularity properties of the solutions.