Boundary blow-up in nonlinear elliptic equations of Bieberbach--Rademacher type
We establish the uniqueness of the positive solution for equations of the form −∆u = au − b(x)f(u) in Ω, u|∂Ω = ∞. The special feature is to consider nonlinearities f whose variation at infinity is not regular (e.g., exp(u) − 1, sinh(u), cosh(u) − 1, exp(u) log(u + 1), uᵝ exp(uᵞ), β ∈ R, γ > 0 or exp(exp(u)) − e) and functions b ≥ 0 in Ω vanishing on ∂Ω. The main innovation consists of using Karamata’s theory not only in the statement/proof of the main result but also to link the...[Show more]
|Collections||ANU Research Publications|
|Source:||Transactions of the American Mathematical Society|
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