A Mixed Local-Nonlocal Hénon Problem in \(\mathbb{R}^{N}\)

Abstract. In this article, we study a Hénon-type equation in [Formula: see text] 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 nonexistence of solutions. Moreover, we establish regularity properties of the solutions.