Uniqueness Of Boundary Blow-up Solutions

In this thesis we study boundary blow-up solutions of quasi-linear elliptic problems. We obtain the exact boundary behaviors of the boundary blow-up solutions on bounded smooth domains. Via boundary strip estimates and the properties of radially symmetric boundary blow-up solutions on balls and annuli. Using the exact boundary behaviors and a comparison principle, we obtain the uniqueness of boundary blow-up solutions of the problems provided some monotonicity assumptions on the nonlinearities.