On the mixed local-nonlocal H\'enon equation

TL;DR

This paper investigates a Hénon-type equation combining local and nonlocal operators, establishing existence, non-existence, and stability results as the fractional parameter approaches 1.

Contribution

It introduces a mixed local-nonlocal Hénon equation and provides new existence, non-existence, and stability results related to classical and fractional cases.

Findings

Existence and non-existence results similar to classical Hénon equations.

Stability of solutions as the fractional parameter approaches 1.

Extension of classical results to a mixed local-nonlocal framework.

Abstract

In this paper we consider a H\'{e}non-type equation driven by a nonlinear operator obtained as a combination of a local and nonlocal term. We prove existence and non-existence akin to the classical result by Ni, and a stability result as the fractional parameter $s \to 1$.