Uniqueness of Nonnegative Solutions for Semipositone Problems on Exterior Domains

Publication Year:
2012
Usage 178
Downloads 170
Abstract Views 8
Repository URL:
https://scholarship.claremont.edu/hmc_fac_pub/498
DOI:
10.1016/j.jmaa.2012.04.005.
Author(s):
Castro, Alfonso; Sankar, Lakshmi; Shivaji, Ratnasingham
Tags:
Uniqueness results; Semipositone problems; Exterior domains; A priori estimates; Mathematics; Physical Sciences and Mathematics
blog post description
We consider the problem−Δu = λK(|x|)f(u), x∈Ωu=0 if |x|=r0u→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.