SELECTED METHODS FOR NONLINEAR BOUNDARY VALUE PROBLEMS, BOGDAN PRZERADZKI, LODZ UNIVERSITY OF TECHNOLOGY MONOGRAPH 2021
Preface
Contents
Chapter 1 Introduction
Chapter 2 Linear BVPs for ODEs
Chapter 3 Topological methods of nonlinear analysis
3.1 Metric fixed points theorems
3.2 Topological fixed points theorems infinite dimension
3.3 Leray-Schauder theory
Chapter 4 Nonlinear BVPs for ODEs
4.1 Using topological degree to simple BVPs
4.2 A priori bounds for derivatives
4.3 Lower and upper solutions
Chapter 5 Resonant problems
5.1 Physical and mathematical notions of resonance
5.2 Perturbation method
5.3 Coincidence degree
Chapter 6 BVP on unbounded domains
6.1 Nonresonant example
6.2 Resonant example
6.3 Perturbation method revisited
Chapter 7 Caratheodory solutions
Chapter 8 Positive solutions
Chapter 9 Variational methods
9.1 Introduction
9.2 Minima of functionals
9.3 Saddle points
Chapter 10 Multiple solutions
10.1 Standard methods
10.2 Applications of the Morse Theory
Chapter 11 BVPs for ODEs in Banach spaces
Chapter 12 Nonlinear BVPs for PDEs
Chapter 13 Miscellaneous exercises
Bibliography
Index