Uniqueness of large radial solutions and existence of nonradial solutions for a superlinear Dirichlet problem in annulii

Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichlet problem in annulii. Our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions. We prove that, for k>0 large, there exist exactly two radial solutions with k nodal regions (connected components of ). The problem need not be homogeneous.