Asymptotic behavior and uniqueness results for boundary blow-up solutions. (English) Zbl 1150.35369

Summary: We estimate the blow-up rate near the boundary and then improve some existing uniqueness results for boundary blow-up solutions to certain quasi-linear elliptic equations with a weight function. The weight function is allowed to vanish on the part of the boundary where the solution blows up. Our approach is based on the construction of certain upper and lower solutions on small annuli with partial boundary blow-up, and on a modified version of an iteration technique due to Safonov.


35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations