Singular semilinear elliptic problems with asymptotically linear reaction terms

We consider the problem {-Delta u = lambda K(x)f(u) in B-1(c), u = 0 on partial derivative B-1, u(x) -> 0 as vertical bar x vertical bar -> infinity where B-1(c) = {x is an element of R-n vertical bar vertical bar x vertical bar > 1}, n > 2, lambda is a positive parameter, K belongs to a class of functions which satisfy certain decay assumptions and f belongs to a class of functions which are asymptotically linear and may be singular at the origin. We prove the existence of positive solutions to such problems for certain values of parameter lambda. Existence results to similar problems in R-n are also obtained. Our existence results are proved using the Schauder fixed point theorem and the method of sub and super solutions. (C) 2020 Published by Elsevier Inc.