Variational approach to various nonlinear problems in geometry and physics

Abstract

In this survey, we will summarize the existence results of nonlinear partial differential equations which arises from geometry or physics by using variational method. We use the method to study Kazdan-Warner problem, Chern-Simons-Higgs model, Toda systems, and the prescribed Q-curvature problem in 4-dimension.

Keywords

Kazdan-Warner problem / Chern-Simons Higgs model / Toda system / Q-curvature

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