On some nonlinear ordinary and partial differential equations.

摘要

This thesis is divided into three chapters. Chapter 1 studies the asymptotic behavior of positive solutions of semilinear elliptic equations with nearly critical nonlinearity. The solutions are shown to blow up at exactly one point. The exact rate and location of blowing up are studied. Chapter 2 studies when a given function can be the Gaussian curvature of a metric which is pointwise conformal to the standard metric on