Department of Mathematics,
Faculty of Physics, MSU
Nonlinear functional analysis and elements of mathematical physics
It is read in the 9-th semester.
2 hours of lectures per week
In the 9th semester continues the study of the geometrical and topological properties of Banach spaces, and presents ideas and methods of nonlinear functional analysis. First of all, we study the properties of such nonlinear mapping is Gateaux differentiable and Frechet, continuity, compactness, it is continuity and complete continuity. Introduces the important concept of Nemytskij operator and Theorem Krasnosel'skii. Then discusses the various variational methods such as the method of Lyusternik-Schnirelmann in conjunction with the principle of compactness of the Palais-Smale, then uses the global bundle Pokhozhaev method sorts the set of Krasnosel'skii in conjunction with the method based on the theorem of the mountain pass. After discusses methods such as the method of compactness, monotonicity and fixed-point theorems. At the end of the course examines the main methods of proof of destruction of solutions of initial and initial-boundary value problems for partial differential equations.
