Non-radially Symmetric Solutions for a Superlinear Ambrosetti-Prodi Type Problem in a Ball

Using a careful analysis of the Morse indices of the solutions obtained by using the Mountain Pass Theorem applied to the associated Euler-Lagrange functional acting both in the full space $H_0^1(\Omega)$ and in its subspace of radially symmetric functions we prove the existence of non-radially symmetric solutions of a problem of Ambrosetti-Prodi type in a ball.