Some useful methods in nonlinear analysis
I plan to select a number of topics in nonlinear elliptic PDEs, Leray Schauder degrees and applications, topological methods in the calculus of variations ( mountain path theorem, Lusternik–Schnirelmann theorem, Morse theory, and applications to nonlinear PDEs), implicit function theorems and applications (including gluing method), ...
, and spend a couple of lectures on each topics. Much of these methods have been used in my own papers, so I should be able to convey to students how to apply these tools...
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Permission by instructor