The asymptotic behaviour of solutions with boundary blow-up for semilinear elliptic equations with nonlinear gradient terms Original Research Article

In this paper, we show existence, uniqueness and exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems Δu±λ|∇u|q=k(x)g(u)Δu±λ|∇u|q=k(x)g(u), x∈Ωx∈Ω, u|∂Ω=+∞u|∂Ω=+∞, where ΩΩ is a bounded domain with smooth boundary in RNRN, λ⩾0λ⩾0, q∈[0,2]q∈[0,2], View the MathML sourcelimd(x)→0k(x)dσ(x)=c0, 0⩽σ<20⩽σ<2, c0>0c0>0, g∈C1[0,∞)g∈C1[0,∞), g(0)=0g(0)=0, g is increasing on (0,∞)(0,∞), and is Karamata regular variation function at infinity with index 1+ρ1+ρ and ρ>0ρ>0.