## Nonlinear Functional Analysis

Time and Place:Vorbesprechung: Do 16. April 2015: 16 Uhr, INF 294, SR 214 |

Abstract:The seminar is devoted to methods for mathematical analysis of nonlinear operators. The main subjects are twofold: fixed-point theorems and a degree theory for operators. The first topic consists of fixed-point theorems starting from Banach fixed-point theorem through Brouwer fixed-point theorem and its generalization to infinite dimensional spaces such as e.g. Leray-Schauder theorem. The second, closely connected, topic of the seminar is the topological degree theory, which is a generalization of the winding number of a curve in the complex plane to mappings between Banach spaces. We will consider the Brouwer degree for finite dimensional Banach spaces and the Leray-Schauder degree for compact mappings in infinite dimensional spaces. Both topics will be illustrated by applications originating from partial differential equations. |

Prerequisites:Analysis I-III, Linear Functional Analysis. The language of the seminar can be English or German depending on the participants. |

Bibliography:[1] K. Deimling, Nonlinear functional analysis, Springer, 1985 [2] L.C. Evans, Partial differential equations, AMS, 3rd Edition 2002 [3] W. Jäger, Nichtlineare Funktionalanalysis, Vorlesungsmanuskript, Heidelberg University, 1996 [4] B. Schweizer, Nichtlineare Analysis, Vorlesungsskript, Basel University, 2005 [5] E. Zeidler, Nonlinear functional analysis and its applications, Vol. I, Springer, 1992 |