The two volumes Nonlinear Functional Analysis and Its Applications, published
in the series Proceedings of Symposia in Pure Mathematics (vol. 45, parts 1 and
2), are the result of the thirty-first Summer Research Institute of the American
Mathematical Society held at the University of California at Berkeley from July
11 to July 29, 1983. This institute was partially supported by a grant from the
National Science Foundation, and organized by an Organizing Committee con-
sisting of Haim Brezis, Felix Browder (Chairman), Tosio Kato, J.-L. Lions, Louis
Nirenberg, and Paul Rabinowitz.
The purpose of the institute was to present and develop research on an
international basis in nonlinear functional analysis and its applications, especially
in the study of boundary value problems for nonlinear partial differential
equations and corresponding problems in geometry and mathematical physics.
Major topics which were covered in a series of expository lectures as well as
research talks included: Minimax methods in the calculus of variations, existence
theory for variational problems without compactness, theories of degree of
mapping, inverse function theorems of Nash-Moser type, nonlinear semigroup
theory, nonlinear equations of evolution, nonlinear problems of control theory,
periodic solutions of Hamiltonian systems, generalizations of the Morse theory,
nonlinear partial differential equations in gauge field theory, the theory of
Feigenbaum cascades, the study of the Navier-Stokes equations, nonlinear el-
liptic equations in differential geometry, and a variety of topics concerning
nonlinear elliptic boundary value and eigenvalue problems, bifurcation theory,
nonlinear hyperbolic equations, nonlinear conservation laws, nonlinear Hamilto-
nian-Jacobi equations, and an even wider variety of physical applications.
There were 13 series of expository lectures totaling 39 hours of lectures which
summarized main directions and methods in current research. In addition, there
were 115 one-hour research lectures.
A total of 203 mathematicians registered for the Institute, twenty of whom were
students. The international character of the Institute is reflected in the national
origins of the participants. Twenty-two countries not in North America were
represented by the following numbers of participants: Africa (1), Australia (3),
Belgium (1), Brazil (1), China (4), Czechoslovakia (1), England (4), France (22),