Schechter M. An introduction to nonlinear analysis

Cambridge University Press, 2004. — 376 p. — (Cambridge Studies in Advanced Mathematics 95). — ISBN: 0-521-84397-9, ISBN13: 9780521843973.The techniques used to solve nonlinear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems and principles from first principles, this textbook gives upper undergraduates and graduate students a thorough understanding using as little background material as possible.Extrema
Critical points
Boundary value problems
Saddle points
Calculus of variations
Degree theory
Conditional extrema
Mini-max methods
Jumping nonlinearities
Higher dimensions
Appendices
Concepts from functional analysis
Measure and integration
Metric spaces
Pseudo-gradients