A mixed local-nonlocal H\'enon problem in $\mathbb{R}^N$

TL;DR

This paper investigates a Hénon-type equation combining local and nonlocal operators in ^N, establishing existence thresholds, non-existence results, and regularity properties of solutions relevant to modeling stellar clusters.

Contribution

It introduces and analyzes a novel mixed local-nonlocal Henon problem, providing existence thresholds and regularity results under specific parameter conditions.

Findings

Existence and non-existence thresholds for solutions.

Regularity properties of solutions.

Relevance to modeling spherically symmetric stellar clusters.

Abstract

In this article, we study a H\'enon-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.