COURSE AIMS AND OBJECTIVES: The goal of the course is to introduce students to further methods of nonlinear analysis: differentiable mappings, method of monotone operators, variational method and to present the applications of the developed theory to the analysis of partial differential equations.
COURSE DESCRIPTION AND SYLLABUS:
- Differentiable mappings, inverse and implicit function theorems, bifurcations (5 weeks)
- Monotone operators, super-solutions and sub-solutions, iterations, variational inequalities (4 weeks)
- Variational methods, extrema, Lagrange multipliers (3 weeks)
- Applications to boundary value problems for partial differential equations (3 weeks).
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