Physical Sciences and Mathematics Commons^™

Existence Of Many Positive Nonradial Solutions For A Superlinear Dirichlet Problem On Thin Annuli, Alfonso Castro, Marcel B. Finan

All HMC Faculty Publications and Research

We study the existence of many positive nonradial solutions of a superlinear Dirichlet problem in an annulus in R^N. Our strategy consists of finding the minimizer of the energy functional restricted to the Nehrai manifold of a subspace of functions with symmetries. The minimizer is a global critical point and therefore is a desired solution. Then we show that the minimal energy solutions in different symmetric classes have mutually different energies. The same approach has been used to prove the existence of many sign-changing nonradial solutions (see [5]).