Math 255C (Spring 2017)
Nonlinear functional analysis.
Instructor: Rowan Killip, 6935 Math Sciences Building.
Prerequisites: Passing the Analysis Qual; or Math 245AB, 246AB, and 255A.
Topics: We will learn the basic techniques in the field by focusing on concrete examples.
- Degree theory.
- Calculus in Banach spaces.
- Geodesics, the principal of least action, Hamiltonian flows.
- Noether's theorem.
- Mountain pass arguments.
- Solitons and nonlinear field equations.
- Periodic orbits in Hamiltonian systems.
- Bifurcation and Lyapunov Schmidt reduction.
Textbook:
- Michael Struwe, Variational Methods. Springer-Verlag, Berlin, 2008.
Available online via UCLA subscription.
Further reading (arranged alphabetically):
- P. Blanchard and E. Brüning, Variational methods in mathematical physics. A unified approach. Springer-Verlag, Berlin, 1992.
- Klaus Deimling, Nonlinear functional analysis. Springer-Verlag, Berlin, 1985.
- Louis Nirenberg, Topics in nonlinear functional analysis. Courant Lecture Notes in Mathematics, 6. American Mathematical Society, Providence, 2001.
- J. T. Schwartz, Nonlinear functional analysis. Gordon and Breach Science Publishers, New York-London-Paris, 1969.