Uniqueness of positive radial solutions for infinite semipositone p-Laplacian problems in exterior domains

We prove uniqueness and asymptotic behavior of positive radial solutions to the p-Laplacian problem {-Delta(p)u = lambda K(vertical bar x vertical bar)f(u) in vertical bar x vertical bar > r(0), u = 0 on vertical bar x vertical bar = r(0), u(x) -> 0 as vertical bar x vertical bar -> infinity, where Omega = {x is an element of R-n : vertical bar x vertical bar > r(0) > 0}, n > p, f : (0, infinity) -> R is continuous, f (u) similar to u(q) at infinity for some q is an element of [0,p - 1) with possible infinite semipositone structure at 0, and lambda is a large parameter. We prove uniqueness and asymptotic behavior of positive radial solutions to the (C) 2018 Elsevier Inc. All rights reserved.