Przeradzki B. Selected Methods for Nonlinear Boundary Value Problems

Lodz: Lodz University of Technology, 2021. — 104 p.Preface
Introduction
Linear BVPs for ODEs
Topological methods of nonlinear analysis
Metric fixed points theorems
Topological fixed points theorems infinite dimension
Leray-Schauder theory
Nonlinear BVPs for ODEs
Using topological degree to simple BVPs
A priori bounds for derivatives
Lower and upper solutions
Resonant problems
Physical and mathematical notions of resonance
Perturbation method
Coincidence degree
BVP on unbounded domains
Nonresonant example
Resonant example
Perturbation method revisited
Caratheodory solutions
Positive solutions
Variational methods
Introduction
Minima of functionals
Saddle points
Multiple solutions
Standard methods
Applications of the Morse Theory
BVPs for ODEs in Banach spaces
Nonlinear BVPs for PDEs
Miscellaneous exercises
Bibliography
Index