Boundary behavior of solutions to some singular elliptic boundary value problems

Let ΩΩ be a bounded domain with smooth boundary in RN(N≥1). For the more general weight bb, some nonlinearities ff and singularities gg, by two kinds of nonlinear transformations, a new perturbation method, which was introduced by García Melián in [J. García Melián, Boundary behavior of large solutions to elliptic equations with singular weights, Nonlinear Anal. 67 (2007) 818–826], and comparison principles, we show that the boundary behavior of solutions to a boundary blow-up elliptic problem Δw=b(x)f(w),w>0,x∈Ω,w|∂Ω=∞Δw=b(x)f(w),w>0,x∈Ω,w|∂Ω=∞ and a singular Dirichlet problem −Δu=b(x)g(u),u>0,x∈Ω,u|∂Ω=0−Δu=b(x)g(u),u>0,x∈Ω,u|∂Ω=0 has the same form under the nonlinear transformations, which can be determined in terms of the inverses of the transformations.