Uniqueness of Large Radial Solutions and Existence of Nonradial Solutions for a Superlinear Dirichlet Problem in Annulii

Authors

Hugo Aduén, Universidad de Cordoba - Colombia
Alfonso Castro, Harvey Mudd CollegeFollow
Jorge Cossio, Universidad Nacional de Colombia

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1-2008

Abstract

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 {x: u(x)≠0}). The problem need not be homogeneous.

Rights Information

© 2008 Elsevier

DOI

10.1016/j.jmaa.2007.03.085

Recommended Citation

Aduén, Hugo; Castro, Alfonso; and Cossio, Jorge, "Uniqueness of Large Radial Solutions and Existence of Nonradial Solutions for a Superlinear Dirichlet Problem in Annulii" (2008). All HMC Faculty Publications and Research. 497.
https://scholarship.claremont.edu/hmc_fac_pub/497