Liouville and Harnack type theorems for semilinear elliptic equations and Yamabe type equations.

摘要

In this dissertation, various semilinear elliptic equations and Yamabe type equations are discussed. We derive Liouville type theorems, Harnack type inequalities and energy estimates for solutions with no singularities. Moreover, for some singular Scalar Curvature equation defined on an open set minus a compact singular set with Newton Capacity zero, we analyze the asymptotic behavior of all its positive solutions near their singularities.