A Primer of Nonlinear Analysis

This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory.

This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems arising from such areas as mechanics and fluid dynamics. The book is intended to accompany upper division courses for students of pure and applied mathematics and physics; exercises are consequently included.

Preface; Preliminaries and notation; 1. Differential calculus; 2. Local inversion theorems; 3. Global inversion theorems; 4. Semilinear Dirichlet problems; 5. Bifurcation results; 6. Bifurcation problems; 7. Bifurcation of periodic solutions; Further reading.

This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory. The book is intended to accompany advanced courses for students of pure and applied mathematics and physics; exercises are consequently included.