| This thesis consists of two parts: In part I we apply the statistical mechanics tech- niques to a generalization of the prescribed Q-curvature problem, especially on the D-dim sphere S D. We introduce a coupling constant c on top of the configurational canonical ensemble and study the weak convergence of this new canonical ensemble. In this part, the Q-curvature does not change sign. In part II the statistical mechanics technique is generalized to the prescribed Q-curvature problem with sign-change, while the mechanical interpretation will be lost. We decompose a single differential equation into a system of two differential equations, and the statistical mechanics technique can be applied to each equation. |
