Uniqueness of Nonnegative Solutions for Semipositone Problems on Exterior Domains

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Lakshmi Sankar, Mississippi State University
Ratnasingham Shivaji, University of North Carolina at Greensboro

Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

10-2012

Abstract

We consider the problem

−Δu = λK(|x|)f(u), x∈Ω

u=0 if |x|=r₀

u→0 as |x|→∞,

where λ is a positive parameter, Δu = div(∇u)is the Laplacian of u, Ω = {x ∈ Rⁿ; n > 2,|x| > r₀}, K ∈ C¹([r₀,∞),(0,∞)) is such that lim r→∞ K(r) = 0 and f ∈ C¹([0,∞),R) is a concave function which is sublinear at ∞ and f(0) < 0. We establish the uniqueness of nonnegative radial solutions when λ is large.

Comments

Author's post-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.1016/j.jmaa.2012.04.005.

Rights Information

© 2012 Elsevier

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/j.jmaa.2012.04.005

Recommended Citation

A. Castro, L. Sankar, R. Shivaji, Uniqueness of nonnegative solutions for semipositone problems on exterior domains, J. Math. Anal. Appl. (2012).