Elliptic equations with general singular lower order term and measure data

In this paper we study a nonlinear elliptic boundary value problem with a general singular lower order term, whose model is {−Δu=H(u)μinΩ,u=0on∂Ω,u>0onΩ, where ΩΩ is an open bounded subset of RNRN, μμ is a nonnegative bounded Radon measure on ΩΩ and HH is a continuous positive function outside the origin such that lims→0+H(s)=+∞. We do not require any monotonicity property on the singular function HH.