Uniqueness of Nonnegative Solutions for Semipositone Problems on Exterior Domains
 Publication Year:
 2012

 Bepress 170

 Bepress 8
 Repository URL:
 https://scholarship.claremont.edu/hmc_fac_pub/498
 DOI:
 10.1016/j.jmaa.2012.04.005.
 Author(s):
 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.