Abstract
The present work has two objectives. First, we prove that a weighted 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 [14, 2008] and [13, 2007] are very useful in our approach.
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