Existence of Many Positive Nonradial Solutions for a Superlinear Dirichlet Problem on thin Annuli

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Marcel B. Finan, University of Texas at Austin

Document Type

Article

Department

Mathematics (HMC)

Publication Date

10-2000

Abstract

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]).

Rights Information

© 2000 Southwest Texas State University

Recommended Citation

Castro, Alfonso and Finan, Marcel B., "Existence of Many Positive Nonradial Solutions for a Superlinear Dirichlet Problem on thin Annuli" (2000). All HMC Faculty Publications and Research. 474.
https://scholarship.claremont.edu/hmc_fac_pub/474