On the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearities

In this paper, we study the existence of positive solutions for the semilinear elliptic problem-Δu+q(·)u-λψ(·,u)u=ϕ(·,u)uinΩ,u>0inΩ,u=0on∂Ω,where λ is a parameter and Ω is a regular bounded domain in Rd. The functions ϕ and ψ are supposed to be locally in the Kato class.