NONLINEAR FUNCTIONAL ANALYSIS

Optional course 4 credits.

 Theory + Exercises: 4 credits

I.  Overview

  Basic methods in nonlinear functional analysis: principle of contractions, topological degree for compact vector fields, fixed points theory, differential calculus in infinity dimensional spaces.

II. Prerequisites : Analysis 1, Analysis2,  Analysis 3,  Functional Analysis.

III. Contents

  Chapter 1 : Fixed points theorems :  Shrinking lemma, the existence and approximation of solutions of  equations of Fredholm and Volterra.

  Chapter 2 : Compacity methods :  Topological degree of compact vector fields. Leray-Schauder fixed point theorem and applications to integral equations.

  Chapter 3 : Differential calculus in normed spaces : Differentiation in normed spaces. Inverse mapping theorem and its applications.

References

[1]   J. Dieudonne , Foundations of modern analysis; Academic Press, New York, 1960.

[2]   Duong Minh Duc,  Functional analysis (Vietnamese);  National University at Hochiminh City Publisher, Hochiminh City,  2000.

[3]   J.T.Schwartz.  Nonlinear Functional analysis and its applications. Vol.I. Springer, New York, 1988.