Large Solutions Of A Class Of Semilinear Elliptic Equations

In this paper,we consider the semilinear elliptic equation:The exitence,uniquness and asymptotic behavior of large solutions are considered.This equation has always been the hotspot in Partial Differential Equation.We notice that the solution blow-up on the boundary,so it is very important to study the asymptotic behavior of large solution.Our framework includes two cases:Ω is a smooth bounded domain in R~N;Ω= R~N .We compare the condition of p and f and summarize the method and tools which are frequently used.We also expound some important proofs in detail.In particular,we discussed that when p(x) = 1,the asymptotic behavior of large solutions is in concern with the mean curvature.