General uniqueness results and variation speed for blow-up solutions of elliptic equations
Florica C. Cîrstea, Yihong Du · Proceedings of the London Mathematical Society · 2005
Let Ω be a smooth bounded domain in RN. We prove general uniqueness results for equations of the form − Δ u = au − b(x) f(u) in Ω, subject to u = ∞ on ∂ Ω. Our uniqueness theorem is established in a setting involving Karamata's theory on regularly varying functions, which is used to relate the blow-up behavior of u(x) with f(u) and b(x), where b ≡ 0 on ∂ Ω and a certain ratio involving b is bounded near ∂ Ω. A key step in our proof of uniqueness uses a modification of an iteration technique due to Safonov. 2000 Mathematics Subject Classification 35J25 (primary), 35B40, 35J60 (secondary).