Newton law corrections and instabilities in f(R) gravity with the effective cosmological constant epoch

We consider class of modified f(R) gravities with the effective cosmological constant epoch at the early and late universe. Such models pass most of solar system tests as well they satisfy to cosmological bounds. Despite their very attractive properties, it is shown that one realistic class of such models may lead to significant Newton law corrections at large cosmological scales. Nevertheless, these corrections are small at solar system as well as at the future universe. Another realistic model with acceptable Newton law regime shows the matter instability.