# The H\'enon problem with large exponent in the disc

## TL;DR

This paper investigates the asymptotic behavior and Morse index of radial solutions to the Hénon problem in a disc with large exponents, leading to multiplicity results for solutions.

## Contribution

It provides the first detailed analysis of the asymptotic profile and Morse index of solutions to the Hénon problem with large exponents in a disc.

## Key findings

- Asymptotic profile of solutions characterized
- Exact Morse index computed for large p
- Multiplicity of solutions established

## Abstract

In this paper we consider the H\'enon problem in the unit disc with Dirichlet boundary conditions. We study the asymptotic profile of least energy and nodal least energy radial solutions and then deduce the exact computation of their Morse index for large values of the exponent p. As a consequence of this computation a multiplicity result for positive and nodal solutions is obtained.