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.
LI Jiayu
. Variational approach to various nonlinear problems
in geometry and physics[J]. Frontiers of Mathematics in China, 2008
, 3(2)
: 205
-220
.
DOI: 10.1007/s11464-008-0013-1
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