EXISTENCE AND UNIQUENESS OF BLOW-UP SOLUTIONS FOR A CLASS OF LOGISTIC EQUATIONS

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Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, background): “⊂ Ω. We denoted by vm the minimal positive solution of (4.41) with Ω 0 replaced by Ωm:= {x∈ Ω : d(x) <1/m}, m≥ m 1. (4.42) We start with the following auxiliary result (see Cˆırstea and Ra˘dulescu [27]). Lemma 4.6. Assume b > 0 on ∂Ω. If (A 1) and (A 2) hold, then for any positive function Φ ∈”
The asymptotic behaviour of the unique solution for the singular Lane–Emden–Fowler equation (2005, methodology): “4) Most recently, applying Karamata regular variation theory, Cîrstea and Rǎdulescu [3–6], Cîrstea [7], Cîrstea and Du [8], the author [34], studied the exact asymptotic behaviour of solutions which blow-up on the boundary for semilinear elliptic problems.”