SUBJECT
Title
Nonlinear functional analysis and its applications
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
4+3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Basic properties of nonlinear operators. Derivatives, potential operators, monotone operators, duality.
Solvability of operator equations. Variational principle, minimization of functionals.
Fixed point theorems. Applications to nonlinear differential equations.
Approximation methods in Hilbert space. Gradient type and Newton-Kantorovich iterative solution methods. Ritz–Galjorkin type projection methods.
Readings
Zeidler, E.: Nonlinear functional analysis and its applications I-III. Kantorovich, L.V., Akilov, G.P.: Functional Analysis