Asymptotic behavior of entire large solutions to semilinear elliptic equations

In this paper, by using Karamata regular variation theory, we study the exact asymptotic behavior of entire large solutions to Δu=b(x)f(u),x∈RN(N≥3), where b∈C(RN) is nonnegative and nontrivial in RN, f∈C([0,∞)) is positive and non-decreasing on (0,∞), which satisfies Keller-Osserman condition and is rapidly varying or regularly varying at infinity with index γ≥1.