Boundary behavior of solutions to some singular elliptic boundary value problems

Abstract Let Ω be a bounded domain with smooth boundary in R N ( N ≥ 1 ) . For the more general weight b , some nonlinearities f and singularities g , by two kinds of nonlinear transformations, a new perturbation method, which was introduced by Garcia Melian in [J. Garcia Melian, 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 Δ w = b ( x ) f ( w ) , w > 0 , x ∈ Ω , w | ∂ Ω = ∞ and a singular Dirichlet problem − Δ u = 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.

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