(1)Course descriptions
<br>   We shall continue the materials in the first semester : Septral theory of compact operators, Sobolev Spaces and variational formulation of elliptic PDE.
<br>Then we shall study the nonlinear functional analysis : Calculus in Banach Space, Implicit function theorem in Banach Space ; Degree Theory in finite and infinite dimesional spaces & Its applications, for examples, Brauer fixed point theorem, Schauder fixed point Theorem ; Bifurcation Thoery : Crandall-Rabinowitz bifurcation from simple eigenvalues.
<br> (2) Text book:
<br>     Haim Brezis: Functional Analysis, Sobolev Spaces, and PDE
<br>     Louis Nirenberg : Topics in Nonlinear Functional Analysis
<br> (3)Reference: 
<br>       Melvin Berger & Marion Berger :Perspectives in Nonlinearity
<br> (4) Teaching Method
<br>     Lectures
<br> (5)Syllabus:
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<br>     For the book of Brezis:
<br>     Chapter 6 :Compact operators. Spetral decomposition of self-adjoint compact operators.
<br>     Chapter 8: Sobolev Spaces and Variational formulation of Boundary Value Problems in one dimension.
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<br>     For the book of Nirenberg
<br>     Chapter I : Topological Approach . Finite dimension
<br>     Chapter II : Topological Degree in Banach Spaces
<br>     Chapter III : Bifurcation Theory
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<br> (6) Evaluations:
<br>     Homework 40%
<br>     Midterm Exam. 30%
<br>     Final Exam. 30%
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