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Topological and variational methods in critical point theory

Course Type: 
PhD Course
Academic Year: 
2016-2017
Period: 
October-January
Duration: 
40 h
Description: 
  • Degree theory
  • Sard's Theorem
  • The Brouwer fixed point theorem with applications
  • The Schauder fixed-point theorem with applications
  • Critical points
  • Differential calculus and critical points; constrained critical points
  • Minimization problems
  • Linear eigenvalues and their variational characterization
  • Ekeland's variational principle
  • The Palais-Smale condition
  • Min-Max methods
  • Linking and Mountain-Pass ¬†theorems
  • Multiplicity via symmetry: the Lusternik-Schnirelamann index
  • Multiplicity via category
  • Applications to elliptic PDE's

Further applications to semilinear nonlinear differential equations will be presented, depending on students' interests and time availability.

Location: 
A-133
Next Lectures: 

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