Bifurcation and symmetry breaking for the Henon equation (Q2016129)

The article investigates the symmetry breaking of radial solutions of the problem \[ -\Delta u = |x|^\alpha u^p \] in the unit ball \(B\) of \(\mathbb{R}^N\) with \(N\geq 3\), \(p>1\), \(0 < \alpha \leq 1\) and with Dirichlet boundary conditions. Using mainly degree theory and investigating a properly modified eigenvalue problem at the radial solution, it is shown, that at least one non-radial solution family bifurcates from the symmetric radial solution and that this branch is unbounded.