Investigations on structures of the solutions to nonlinear elliptic partial differential equations on the sphere.

点击翻译按钮获取中文摘要

In this research period, I investigated the imperfect bifurcations on azimuthal solutions to a nonlinear elliptic equation when the domain covers almost the whole sphere and showed how the structure of bifurcations asymptotically looked like. As for the cases including non-azimuthal solutions, I obtained some results just before the end of the term. Also, as a related topics, I studies the behavior of solutions to a heat equation with a potential and showed that the time global behavior was governed by solutions to the stationary problem.