1. Background. Elements of Functional Analysis. Differential Calculus in Banach Spaces.
2. Fixed Point Existence Theory.
3. Degree Theory. Brouwer Degree. Leray-Schauder Degree.
4. The Krasnoselskii-Rabinowitz Bifurcation Theorem. Applications to PDE.
Bibliography
1. H. W. Alt, Lineare Funktionalanalysis, Springer-Lehrbuch, Berlin, 1992.
2. R. F. Brown, A Topological Introduction to Nonlinear Analysis, Birkhäuser, Basel, 1993.
3. C.P. Niculescu, Special Topics in Functional Analysis, Universitaria Press, Craiova, 2005.
4. E. Zeidler, Nonlinear Functional Analysis and Its Applications: Fixed point Theorems,
Springer-Verlag, 1986.