Bifurcation and symmetry breaking for the H\'enon equation

TL;DR

This paper investigates the Hénon equation within a ball, demonstrating the existence of nonradial solutions that bifurcate from radial solutions and showing that this solution branch extends infinitely.

Contribution

It establishes the bifurcation of nonradial solutions from radial solutions in the Hénon problem, revealing an unbounded branch of solutions.

Findings

Existence of nonradial solutions bifurcating from radial solutions.

The bifurcating branch is unbounded.

Provides mathematical proof of bifurcation phenomena.

Abstract

In this paper we consider the H\'enon problem in a ball. We prove the existence of (at least) one branch of nonradial solutions that bifurcate from the radial ones and that this branch is unbounded.