This volume contains a number of research-expository articles that appeared in the Bulletin of the ""AMS"" between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and geometry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of applications. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers in the field.
General theory Lectures on Morse Theory, old and new by R. Bott Fixed point theory and nonlinear problems by F. E. Browder Nonconvex minimization probems by I. Ekeland Variational and topological methods in nonlinear problems by L. Nirenberg The inverse function theorem of Nash and Moser by R. S. Hamilton Applications The influence of elasticity on analysis: modern developments by S. S. Antman Periodic solutions of nonlinear vibrating strings and duality principles by H. Brezis Bifurcation and symmetry breaking in applied mathematics by D. H. Sattinger Non-Euclidean functional analysis and electronics by J. W. Helton Dynamical systems The dynamical systems approach to differential equations by M. W. Hirsch The fundamental theorem of algebra and complexity theory by S. Smale Complex analytic dynamics on the Riemann sphere by P. Blanchard Discrete conformal groups and measurable dynamics by D. Sullivan.