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

Pablo Ochoa; Ariel Salort

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arXiv · 2512.09794

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

Pablo Ochoa·Ariel Salort

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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.

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Pablo Ochoa, Ariel Salort. 2025-12-10. A mixed local-nonlocal H\'enon problem in $\mathbb{R}^N$. https://arxiv.org/abs/2512.09794

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