  The present work has two objectives. First, we prove that a weight\-ed
superlinear elliptic problem has infinitely many nonradial solutions in the
unit ball. Second, we obtain the same conclusion in annuli for a more general
nonlinearity which also involves a weight. We use a lower estimate of the
energy level of radial solutions with $k-1$ zeros in the interior of the domain
and a simple counting. Uniqueness results due to Tanaka \cite[2008]{Tanaka1}
and \cite[2007]{Tanaka2} are very useful in our approach.
