We study the steady-state properties of the long-range one-species reaction A + A --> 0 in d-dimensional systems with an external random input of A particles. Particles are immobile and react via transfer rates dependent on the interparticle distance : For different forms of these transfer rates we calculate exactly, in form of bounds, the steady-state density of A particles. We show that they are described by the nonclassical dependence on the input rate and the parameters of the transfer rate. Our analytical results are in good agreement with experiments on excimer quenching and Monte Carlo simulation data.