Singular semilinear elliptic problems with asymptotically linear reaction terms

Abstract

We consider the problem{−Δu=λK(x)f(u)in B1c,u=0on ∂B1,u(x)→0as |x|→∞, where B1c={x∈Rn||x|>1},n>2, λ 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 λ. Existence results to similar problems in Rn are also obtained. Our existence results are proved using the Schauder fixed point theorem and the method of sub and super solutions.