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Asymptotic behavior of positive solutions of a singular nonlinear Dirichlet problem. (English) Zbl 1196.35109
Summary: Let 𝛺 be a C 1,1 -bounded domain in n for n2. In this paper, we are concerned with the asymptotic behavior of the unique positive classical solution to the singular boundary-value problem Δu+a(x)u -σ =0 in 𝛺, u |𝛺 =0, where σ0, a is a nonnegative function in C loc α (𝛺), 0<α<1 and there exists c>0 such that 1 ca(x)(δ(x)) λ k=1 m (Log k (ω δ(x))) μ k c. Here, λ2,μ k , ω is a positive constant and δ(x)=dist(x,𝛺).
MSC:
35J75Singular elliptic equations
35J25Second order elliptic equations, boundary value problems
35B09Positive solutions of PDE
35B40Asymptotic behavior of solutions of PDE
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